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# Words that Describe Patterns

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Words that Describe Patterns

While working at the zoo one day, Joshua saw a customer drop her purse and a whole pile of change came flooding out of it. Joshua ran over to help and immediately began picking up all kinds of coins. It seems that the clasp of the woman's change purse had snapped and sent money rolling over the ground.

Joshua picked up 30 pennies, 15 nickels, 10 dimes and 13 quarters. The woman was very grateful, and Joshua was glad that he had been there to help out.

When he was walking away, Joshua wondered how much money the woman had dropped. This is a perfect example of where a real - world problem and expressions can come in handy.

Pay close attention to this Concept and you will learn how to write an expression and solve for the sum of the money.

### Guidance

Money is a common source of dilemmas in real - life. Let's combine money and variable expressions to solve a real - world problem.

Joanne has a pile of nickels and a pile of dimes. She counts her money and figures out that she has 25 nickels and 36 dimes. Given these counts, how much money does Joanne have in all?

The first thing that we need to do is to underline all of the important information in the problem.

Joanne has a pile of nickels and a pile of dimes. She counts her money and figures out that she has 25 nickels and 36 dimes. Given these counts, how much money does Joanne have in all?

Next, we need to write an expression with a variable.

$.05x +.10y$

A nickel is 5 cents. We can use decimal .05 to show that amount in dollars.

A dime is 10 cents. We can use decimal .10 to show that amount in dollars.

The $x$ represents the number of nickels.

The $y$ represents the number of dimes.

We have been given the number of dimes and nickels that Joanne has. We can substitute those values into our expression for $x$ and $y$ .

$.05(25) + .10(36)$

Next, we evaluate the expression.

$1.25 + 3.60 = \4.50$

Joanne has $\4.50$ total. You can see why we changed the way we wrote the value of coins from cents to dollars now, because our answer is in dollars.

Use the expression that Joanne used to figure out the following totals.

#### Example A

If you have 6 nickels and five dimes, what is the sum?

$.05x +.10y$

Solution: .80

#### Example B

If you have 15 nickels and 20 dimes, what is the sum?

$.05x +.10y$

Solution: $2.75 #### Example C If you have 35 nickels and 40 dimes, what is the sum? $.05x +.10y$ Solution:$5.75

These examples are the perfect practice for helping Joshua with his dilemma. Let's look at the original problem once again.

While working at the zoo one day, Joshua saw a customer drop her purse and a whole pile of change came flooding out of it. Joshua ran over to help and immediately began picking up all kinds of coins. It seems that the clasp of the woman's change purse had snapped and sent money rolling over the ground.

Joshua picked up 30 pennies, 15 nickels, 10 dimes and 13 quarters. The woman was very grateful, and Joshua was glad that he had been there to help out.

When he was walking away, Joshua wondered how much money the woman had dropped.

First, Joshua will need to write an expression to explain the money that was found. Joshua picked up pennies, nickels, dimes and quarters. Begin by writing the worth of each coin in the expression.

$.01x +.05y + .10z + .25q$

Next, substitute the number of each coin found.

$.01(30) +.05(15) + .10(10) + .25(13)$

Finally, evaluate the expression for the sum of the dropped money.

The answer is $\5.30$ .

### Vocabulary

Evaluate
to simplify an expression that does not have an equals sign.
Variable
a letter, usually lowercase, that is used to represent an unknown quantity.
Expression
a number sentence that uses operations but does not have an equals sign
Variable Expression
a number sentence that has variables or unknown quantities in it with one or more operations and no equals sign.

### Guided Practice

Here is a problem for you to try on your own. Use the given information to write an expression and solve for the sum.

Imagine that you have found a pile of money in a drawer. In it, you have 10 nickels, 5 dimes and 15 quarters. How much is the sum of the money that you have found?

First, you have to write an expression. Nickels are worth .05, dimes are worth .10 and quarters are worth .25. Now you can write an expression.

$.05x +.10y + .25z$

Next, you can substitute in the numbers of each coin that we found. You found 10 nickels, 5 dimes and 15 quarters.

$.05(10) +.10(5) + .25(15)$

$.50 + .50 + 3.75$

Our total is $\4.75$ .

### Practice

Directions: Write an expression for each money amount and evaluate it by using the given information.

1. 15 quarters

2. 10 dimes and 3 quarters

3. 30 nickels and 15 dimes

4. 6 quarters and 60 nickels

5. 21 quarters and 14 dimes

6. 6 dimes, 10 nickels and 120 pennies

7. 18 quarters and 12 half - dollars.

8. 32 dimes, 16 nickels and 11 quarters

9. 18 nickels, 33 dimes and 39 quarters

10. 27 dimes, 87 pennies, 12 quarters

11. 10 pennies, 15 nickels, 9 dimes and 27 quarters

12. 35 quarters and 98 nickels

13. 95 dimes, 27 nickels and 82 quarters

14. 77 dimes, 15 nickels and 81 quarters

15. 70 nickels, 63 dimes, 82 pennies and 55 quarters

16. 12 nickels, 33 dimes, 17 pennies and 80 quarters

### Vocabulary Language: English

$\ge$

$\ge$

The greater-than-or-equal-to symbol "$\ge$" indicates that the value on the left side of the symbol is greater than or equal to the value on the right.
$\le$

$\le$

The less-than-or-equal-to symbol "$\le$" indicates that the value on the left side of the symbol is lesser than or equal to the value on the right.
$\ne$

$\ne$

The not-equal-to symbol "$\ne$" indicates that the value on the left side of the symbol is not equal to the value on the right.
constant

constant

A constant is a value that does not change. In Algebra, this is a number such as 3, 12, 342, etc., as opposed to a variable such as x, y or a.
Equation

Equation

An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs.
Evaluate

Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.
Expression

Expression

An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.
greater than

greater than

The greater than symbol, $>$, indicates that the value on the left side of the symbol is greater than the value on the right.
greater than or equal to

greater than or equal to

The greater than or equal to symbol, $\ge$, indicates that the value on the left side of the symbol is greater than or equal to the value on the right.
inequality

inequality

An inequality is a mathematical statement that relates expressions that are not necessarily equal by using an inequality symbol. The inequality symbols are $<$, $>$, $\le$, $\ge$ and $\ne$.
less than

less than

The less-than symbol "<" indicates that the value on the left side of the symbol is lesser than the value on the right.
less than or equal to

less than or equal to

The less-than-or-equal-to symbol "$\le$" indicates that the value on the left side of the symbol is lesser than or equal to the value on the right.
not equal to

not equal to

The "not equal to" symbol, $\ne$, indicates that the value on the left side of the symbol is not equal to the value on the right.
Variable

Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.
Variable Expression

Variable Expression

A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.