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# 7.9: Save More

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Look at the signs for the toothpaste below. How much would it cost to buy 2 tubes of toothpaste at each store? What if you use the coupon? Which store has the better buy? How much less is the cost at that store? In this concept, we will learn how to compare prices at stores when we have a coupon to use.

### Guidance

In order to figure out which item is the better buy, like in the question above, we can use the problem solving steps to help.

• Start by describing what you see the pictures.
• Next, figure out what your job is in this problem. In all of these problems your job will be to figure out which item is the better buy and by how much.
• Then, make a plan for how you will solve. In these problems, you will want to figure out the original cost for the number of items you want to buy at each store. Then, calculate how much you will pay after using the coupon. Finally, figure out which store has the better buy and by how much.
• Next, solve the problem.
• Finally, check to make sure that all your calculations are correct.

#### Example A

Buy 1 comb. Use the coupon. Which store has the better buy? How much less is the cost at that store?

Solution:

We can use problem solving steps to help.

Step Description
Describe: Two store signs show the cost for combs. The coupon gives 10% off the price.
My Job: Figure out the store that has the better buy for 1 comb after using the coupon. Then figure out the difference in cost.
Solve: ABC's: 5 combs are $15 so each comb is$3. Gem's: 6 combs are $12 so each comb is$2. Using the coupon at ABC's, 10% off means the cost after the coupon is 90% of $3.00, or 0.9 × 3 =$2.70. Using the coupon at Gem's, 10% off means the price after the coupon is 90% of $2.00 or 0.9 × 2 =$1.80. $2.70 −$1.80 = $0.90 The cost is$0.90 less at Gem's.
Check:

At ABC's 1 comb is $3.00 and 10% off of$3.00 is $0.30. The cost after using the coupon is ($3.00 - $0.30), or$2.70. At Gem's 1 comb is $2.00 and 10% off of$2.00 is $0.20. The cost after using the coupon is ($2.00 - $0.20), or$1.80. $2.70 −$1.80 = $0.90. #### Example B Buy 4 boxes of band aids. Use the coupon. Which store has the better buy? How much less is the cost at that store? Solution: We can use problem solving steps to help. $& \mathbf{Describe:} && \text{Two store signs show the cost for boxes of bandaids. The coupon gives}\\&&& 30 \% \ \text{off the price.}\\& \mathbf{My \ Job:} && \text{Figure out the store that has the better buy for 4 boxes of band aids after}\\&&& \text{using the coupon. Then figure out the difference in cost.}\\& \mathbf{Plan:} && \text{Figure out the cost of 4 boxes of tissue at ABC's. Do the same at Gem's.}\\&&& \text{Take 30\% off of each. Subtract to find the difference.}\\& \mathbf{Solve:} && \text{ABC's:} \ 6 \ \text{boxes are} \ \12 \ \text{so each box is} \ \2 \ \text{and four boxes are} \ \8.\\&&& \text{Gem's:} \ 8 \ \text{boxes are} \ \24 \ \text{so} \ 4 \ \text{boxes are} \ \frac{1}{2} \ \text{of} \ 24, \ \text{or} \ \24 \div 2, \ \text{or} \ \12.\\&&& \text{Using the coupon at ABC's,} \ 30 \% \ \text{off means the cost after the coupon is}\\&&& 70 \% \ \text{of} \ \8.00, \ \text{or} \ 0.3 \times 8 = \5.60.\\&&& \text{Using the coupon at Gem's,} \ 20 \% \ \text{off means the price after the coupon is}\\&&& 70 \% \ \text{of} \ \12.00 \ \text{or} \ 0.3 \times 12 = \8.40.\\&&& \8.40 - \5.60 = \2.80\\&&& \text{The cost is} \ \2.80 \ \text{less at ABC's.}\\& \mathbf{Check:} && \text{At ABC's} \ 4 \ \text{boxes are} \ \8.00 \ \text{and} \ 30 \% \ \text{off of} \ \8.00 \ \text{is} \ \2.40. \ \text{The cost after}\\&&& \text{using the coupon is} \ \8.00 - \2.40, \ \text{or} \ \5.60.\\&&& \text{At Gem's} \ 4 \ \text{boxes are} \ \12.00 \ \text{and} \ 30 \% \ \text{off of} \ \12.00 \ \text{is} \ \3.60. \ \text{The cost after}\\&&& \text{using the coupon is} \ \12.00 - \3.60, \ \text{or} \ \8.40. \ \8.40 - \5.60 = \2.80.$ #### Example C Buy 2 boxes of tissue. Use the coupon. Which store has the better buy? How much less is the cost at that store? Solution: We can use problem solving steps to help. $& \mathbf{Describe:} && \text{Two store signs show the cost for boxes of tissue. The coupon gives}\\&&& 20 \% \ \text{off the price.}\\& \mathbf{My \ Job:} && \text{Figure out the store that has the better buy for 2 boxes of tissue after}\\&&& \text{using the coupon. Then figure out the difference in cost.}\\& \mathbf{Plan:} && \text{Figure out the cost of 2 boxes of tissue at ABC's. Do the same at Gem's.}\\&&& \text{Take 20\% off of each. Subtract to find the difference.}\\& \mathbf{Solve:} && \text{ABC's:} \ 4 \ \text{boxes are} \ \12 \ \text{so} \ 2 \ \text{boxes are half the price or} \ \6.\\&&& \text{Gem's:} \ 6 \ \text{boxes are} \ \24 \ \text{so} \ 2 \ \text{boxes are} \ \frac{1}{3} \ \text{of} \ 24, \ \text{or} \ \24 \div 3, \ \text{or} \ \8.\\&&& \text{Using the coupon at ABC's,} \ 20 \% \ \text{off means the cost after the coupon is}\\&&& 80 \% \ \text{of} \ \6.00, \ \text{or} \ 0.8 \times 6 = \4.80.\\&&& \text{Using the coupon at Gem's,} \ 20 \% \ \text{off means the price after the coupon is}\\&&& 80 \% \ \text{of} \ \8.20 \ \text{or} \ 0.8 \times 8 = \6.40.\\&&& \6.40 - \4.80 = \1.60\\&&& \text{The cost is} \ \1.60 \ \text{less at ABC's.}\\& \mathbf{Check:} && \text{At ABC's} \ 2 \ \text{boxes are} \ \6.00 \ \text{and} \ 20 \% \ \text{off of} \ \6.00 \ \text{is} \ \1.20. \ \text{The cost after}\\&&& \text{using the coupon is} \ \6.00 - \1.20, \ \text{or} \ \4.80.\\&&& \text{At Gem's} \ 2 \ \text{boxes are} \ \8.00 \ \text{and} \ 20 \% \ \text{off of} \ \8.00 \ \text{is} \ \1.60. \ \text{The cost after}\\&&& \text{using the coupon is} \ \8.00 - \1.60, \ \text{or} \ \6.40. \ \6.50 - \4.80 = \1.60.$ #### Concept Problem Revisited We can use problem solving steps to help. $& \mathbf{Describe:} & & \text{Two store signs show the cost for tubes of toothpaste. The coupon gives}\\ & & & 20 \% \ \text{off the price.}\\ & \mathbf{My \ Job:} && \text{Figure out the store that has the better buy for 2 tubes of toothpaste after}\\ & & & \text{using the coupon. Then figure out the difference in cost.}\\ & \mathbf{Plan:} && \text{Figure out the cost of 2 tubes of toothpaste ABC's. Do the same at Gem's.}\\ & & & \text{Take 20\% off of each. Subtract to find the difference.}\\ & \mathbf{Solve:} && \text{ABC's:} \ 4 \ \text{tubes are} \ \6 \ \text{so} \ 2 \ \text{tubes are half the price or} \ \3.\\ & & & \text{Gem's:} \ 10 \ \text{tubes are} \ \16 \ \text{so} \ 2 \ \text{tubes are} \ \frac{1}{5} \ \text{of} \ 16, \ \text{or} \ \16 \div 5, \ \text{or} \ \3.20.\\ & & & \text{Using the coupon at ABC's,} \ 20 \% \ \text{off means the cost after the coupon is}\\ & & & 80 \% \ \text{of} \ \3.00, \ \text{or} \ 0.8 \times 3 = \2.40.\\ & & & \text{Using the coupon at Gem's,} \ 20 \% \ \text{off means the price after the coupon is}\\ & & & 80 \% \ \text{of} \ \3.20 \ \text{or} \ 0.8 \times 3.20 = \2.56.\\ & & & \2.56 - \2.40 = \0.16\\ & & & \text{The cost is} \ \0.16 \ \text{less at ABC's.}\\ & \mathbf{Check:} && \text{At ABC's} \ 2 \ \text{tubes are} \ \3.00 \ \text{and} \ 20 \% \ \text{off of} \ \3.00 \ \text{is} \ \0.60. \ \text{The cost after}\\ & & & \text{using the coupon is} \ \3.00 - \0.60, \ \text{or} \ \2.40.\\ & & & \text{At Gem's} \ 2 \ \text{tubes are} \ \3.20 \ \text{and} \ 20 \% \ \text{off of} \ \3.20 \ \text{is} \ \0.64. \ \text{The cost after}\\ & & & \text{using the coupon is} \ \3.20 - \0.64, \ \text{or} \ \2.56. \ \2.56 - \2.40 = \0.16.$ ### Vocabulary A discount is a savings on an item because of a sale or a coupon. In this concept, we used coupons that had discounts in the form of percents of. Percent means parts per 100. The symbol for percent is %. For example, 30% means 30 out of every 100. So, 30% of 100 would be 30. 30% of 50 would be 15. When working with percents, it is often helpful to convert them to decimals when doing calculations, as we did in this concept. ### Guided Practice 1. Buy 2 toothbrushes. Use the coupon. Which store has the better buy? How much less is the cost at that store? 2. Buy 4 bars of soap. Use the coupon. Which store has the better buy? How much less is the cost at that store? 3. Buy 4 bottles of shampoo. Use the coupon. Which store has the better buy? How much less is the cost at that store? Answers: 1. Gems;$0.25 less.

ABC's: 1 toothbrush is $5.25 \div 3$ or $1.75, so 2 toothbrushes are$3.50. With the coupon they are $0.5 \times 3.50$ , or $1.75. Gem's: 2 toothbrushes is half of$6.00, or $3.00. With the coupon they are $0.5 \times 3.00$ , or$1.50.
$1.75-$1.50=$0.25 2. ABC's:$0.28 less.

ABC's: 4 bars of soap are $\frac {1}{2}$ of $7.20, or$3.60. With the coupon, they are $0.7 \times 3.60$ , or $2.52. Gem's: 10 bars for$10 is $1 for one bar and$4 for 4 bars. With the coupon they are $0.7 \times 4.00$ or $2.80.$2.80-$2.52=$0.28

3. Gem's: $0.24 less. ABC's: One bottle is $12.50 \div 5$ or$2.50, so 4 bottles is $4 \times 2.50$ or $10. With the coupon, the bottles are $0.6 \times 10$ or$6.00.
Gem's: One bottle is $14.40 \div 6$ or $2.40, so 4 bottles is $4 \times 2.40$ or$9.60. With the coupon, the bottles are $0.6 \times 9.60$ , or $5.76.$6.00-$5.76=$0.24

### Practice

1. Buy 2 birdies. Use the coupon. Which store has the better buy? How much less is the cost at that store?

2. Buy 5 water bottles with straws. Use the coupon. Which store has the better buy? How much less is the cost at that store?

3. Buy 2 mugs. Use the coupon. Which store has the better buy? How much less is the cost at that store?

4. Buy 4 boxes of paperclips. Use the coupon. Which store has the better buy? How much less is the cost at that store?

5. Buy 3 notebooks. Use the coupon. Which store has the better buy? How much less is the cost at that store?

Jan 18, 2013