Christina has three more quarters than dimes. The total value of the dimes and quarters is $13....

Question:

Christina has three more quarters than dimes. The total value of the dimes and quarters is $13. How many quarters does she have?

Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

For example: 4x +3y = 1 is an algebraic equation where x and y are variables and 1 is the equivalent constant of the relation shown in the equation.

In the word problems of algebraic equation, this relation is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

Answer and Explanation:

Let the number of dimes and quarters with Christina is {eq}D {/eq} and {eq}Q. {/eq}

According to the question Christina has three more quarters than dimes

$$Q= D +3 $$

Total value is {eq}$13. {/eq}

$$0.25Q + 0.10D = 13 $$

Using value of {eq}Q = D +3 {/eq}

$$0.25(D+3) + 0.10D = 13 $$

$$0.25D+0.75 + 0.10D = 13 $$

$$0.35D = 13 -0.75 $$

$$0.35D = 12.25 $$

$$D = 35 $$

$$Q = D +3 $$

$$Q = 38 $$

Number of quarters with Christina is {eq}38 {/eq}


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