Question

Hands on: Francesca has quarters and dimes that equal $1.15. She has 1 more dime than quarters. How many quarters and dimes does she have?

Answer 1

To solve this problem we need to use the conditions to write an equation, so Q will be the number of quarters and D will be the number of dimes so the first condition is:

the sum of quartes (0.25) plus dimes (0.10) are $1.15

`Q(0.25)+D(0.10)=1.15`

the second condition is; she has one more dimes than quarters so:

`Q+1=D`

So we can replace the secon equation into the first equation so:

`Q(0.25)+(Q+1)(0.10)=1.15`

Now we can simplify the equation so:

`0.25Q+0.10Q+0.10=1.15`

And finally we solve for Q so:

`\begin{gathered} 0.35Q=1.15-0.10 \\ 0.35Q=1.05 \\ Q=(1.05)/(0.35) \\ Q=3 \end{gathered}`

Now we can replace the value of Q in the second equation so:

`\begin{gathered} D=Q+1 \\ D=3+1 \\ D=4 \end{gathered}`

So Francesca have 3 quarters and 4 dimes