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### Stems of Linear Equations: Tutorial

#### Warm-Up

Sometimes, more than one expression can describe the same situation.

Suppose you have a pocketful of change. You have some pennies [tex]\((p)\)[/tex] and some quarters [tex]\((q)\)[/tex].

1. One expression describes the total number of coins in your pocket:
[tex]\[ p + q \][/tex]

2. A second expression describes the amount of money (in dollars) in your pocket:
[tex]\[ 0.01p + 0.25q \][/tex]

Notice that each expression describes a different characteristic of the change in your pocket.

Evaluate each expression for the situation where you have 6 quarters and 7 pennies in your pocket.

Type the correct answer in each box. Use numerals instead of words.

- The number of coins is [tex]\( p + q = \square \)[/tex]
- The amount of money is [tex]\( 0.01p + 0.25q = \square \)[/tex]



Answer :

GinnyAnswer
Sure! Let's solve this step-by-step.

1. Total Number of Coins:
- Here, [tex]\( p \)[/tex] (the number of pennies) is 7.
- And [tex]\( q \)[/tex] (the number of quarters) is 6.
- The total number of coins is the sum of pennies and quarters.
[tex]\[ p + q = 7 + 6 \][/tex]
[tex]\[ p + q = 13 \][/tex]

So, the number of coins is [tex]\( 13 \)[/tex].

2. Total Amount of Money:
- Each penny is worth [tex]$0.01. - Each quarter is worth $[/tex]0.25.
- The amount of money contributed by the pennies is [tex]\( 0.01 \times 7 \)[/tex].
- The amount of money contributed by the quarters is [tex]\( 0.25 \times 6 \)[/tex].
[tex]\[ 0.01p + 0.25q = 0.01 \times 7 + 0.25 \times 6 \][/tex]
[tex]\[ 0.01p + 0.25q = 0.07 + 1.50 \][/tex]
[tex]\[ 0.01p + 0.25q = 1.57 \][/tex]

So, the amount of money is [tex]\( 1.57 \)[/tex].

In conclusion:
- The number of coins is [tex]\( 13 \)[/tex].
- The amount of money is [tex]\( 1.57 \)[/tex].

Type these numbers in the boxes provided:
- The number of coins is [tex]\( 13 \)[/tex].
- The amount of money is [tex]\( 1.57 \)[/tex].