I have 18 bills that equal $100.00 (5-$10 bills, 9-$5 bills, 3-$1 bills, 1-$2 bill). How can this...

Question:

I have {eq}18 {/eq} bills that equal {eq}\$100.00 {/eq} (5-{eq}\$10 {/eq} bills, 9-{eq}\$5 {/eq} bills, 3-{eq}\$1 {/eq} bills, 1-{eq}\$2 {/eq} bill). How can this be expressed in an algebraic equation?

Algebraic Expressions:

Algebraic expressions are used to translate words to their mathematical equivalent. Typically, the first step to writing an algebraic expression to define the unknown variables of the given problem. Then each part of the sentence can be logically translated using these variables.

Answer and Explanation:

Denote the follow variables for the bill amounts:

{eq}T {/eq} stands for the total number of $10

{eq}F {/eq} stands for the total number of $5

{eq}O {/eq} stands for the total number of $1

{eq}W {/eq} stands for the total number of $2

Then, since the total number of bills is 18,

{eq}18 = T+F+O+W {/eq}

Also, the total value of the bills equals $100,

{eq}100 = 10\cdot T + 5\cdot F + 1 \cdot O + 2\cdot W {/eq}

Since we know the values of the variables, we can double check the algebraic equations.

{eq}T = 5, ~ F = 9, ~ O = 3, ~ W = 1 {/eq}

{eq}18 = T+F+O+W \quad \implies \quad 18 = 5+9+3+1 \checkmark {/eq}

{eq}100 = 10\cdot T + 5\cdot F + 1 \cdot O + 2\cdot W \quad \implies \quad 100 =10\cdot 5 + 5\cdot 9 + 1 \cdot 3 + 2\cdot 1 = 50 + 45 + 3 + 2 \checkmark {/eq}


Learn more about this topic:

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Translating Words to Algebraic Expressions

from Algebra I: High School

Chapter 8 / Lesson 17
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