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Save More - Reason Proportionally with Percents

Teacher Notes

Students are presented with prices of sets of items at two different stores, and a coupon that can be applied to the purchase at both stores. To determine the better buy, students first reason proportionally to figure out the costs of the items at each store. Then, they apply the coupon in order to determine the discounted cost, and compare those costs to figure out the savings.

To determine the total cost after applying the coupon, students may use either a one- or two-step process. On the teaching page, we use the one-step process in the Solve step and the two-step process in the Check step. For example, if an item is discounted 10%, then its new price is 90% of the original price. So, multiplying the original price by 0.9 will give the discounted price using one computational step. For the two-step method, the discount is taken first (10% of the original price is the discount). For the second step, the amount of the discount is subtracted from the original price to get the discounted price.

Solutions

1. \quad \text{Gem's;} \ \$.90 \ \text{less}\!\\ {\;} \quad \ \text{ABC's:} \ 1 \ \text{comb is} \ \$15 \div 5, \ \text{or} \ \$3\!\\{\;} \quad \ \text{With the coupon the cost is} \ 0.9 \times \$3, \ \text{or} \ \$2.70\!\\{\;} \quad \ \text{Gem's:} \ 1 \ \text{comb is} \ \$12 \div 6, \ \text{or} \ \$2\!\\{\;} \quad \ \text{With the coupon the cost is} \ 0.9 \times \$2, \ \text{or} \ \$1.80\!\\  {\;} \quad \ \$2.70 - \$1.80 = \$0.90

2. \quad \text{ABC's;} \ \$2.80 \ \text{less}\!\\{\;} \quad \ \text{ABC's:} \ 6 \ \text{boxes for} \ \$12 \ \text{is} \ 1 \ \text{box for} \ \$2.\!\\{\;} \quad \ 4 \times \$2 \ \text{is} \ \$8 \ \text{for} \ 4 \ \text{boxes}\!\\{\;} \quad \ \text{With the coupon the cost is} \ 0.7 \times \$8, \ \text{or} \ \$5.60\!\\{\;} \quad \ \text{Gem's:} \ 4 \ \text{boxes is half of} \ \$24, \ \text{or} \ \$12\!\\{\;} \quad \ \text{With the coupon the cost is} \ 0.7 \times \$12, \ \text{or} \ \$8.40\!\\{\;} \quad \ \$8.40 - \$5.60 = \$2.80

3. \quad \text{ABC's;} \ \$1.60 \ \text{less}\!\\{\;} \quad \ \text{ABC's:} \ 4 \ \text{boxes for} \ \$12 \ \text{is} \ 2 \ \text{boxes for} \ \$6\!\\{\;} \quad \ \text{With the coupon, the cost is} \ 0.8 \times \$6 \ \text{or} \ \$4.80\!\\{\;} \quad \ \text{Gem's:} \ 6 \ \text{boxes for} \ \$24 \ \text{is} \ 2 \ \text{boxes for} \ \$8\!\\{\;} \quad \ \text{With the coupon, the cost is} \ 0.8 \times 8, \ \text{or} \ \$6.40\!\\{\;} \quad \ \$6.40 - \$4.80 = \$1.60

Buy 2 tubes of toothpaste. Use the coupon. Which store has the better buy? How much less is the cost at that store?

& \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. Take 20\% off of each.}\\&&& \text{Do the same at Gem's. 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.

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

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

Buy 2 boxes of tissue. Use the coupon. Which store has the better buy? How much less is the cost at that store

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