Question

question
logan has $3.15 worth of dimes and quarters. he has twice as many dimes as quarters.
determine the number of dimes and the number of quarters that logan has.

answer attempt 1 out of 2

there are 　 dimes and 　 quarters.

Explanation:

Step1: Define variables

Let the number of quarters be $q$. Then the number of dimes is $2q$ (since there are twice as many dimes as quarters).

Step2: Write the value equation

A quarter is worth $0.25$ dollars and a dime is worth $0.10$ dollars. The total value is $3.15$ dollars. So the equation is: $0.25q + 0.10(2q)=3.15$

Step3: Simplify and solve for $q$

First, simplify the left - hand side: $0.25q+0.20q = 3.15$. Combine like terms: $0.45q=3.15$. Then divide both sides by $0.45$: $q=\frac{3.15}{0.45}=7$.

Step4: Find the number of dimes

Since the number of dimes is $2q$, substitute $q = 7$ into it. So the number of dimes is $2\times7 = 14$.

Answer:

There are $\boldsymbol{14}$ dimes and $\boldsymbol{7}$ quarters.