Question

3. Jeff has 12 coins that have a total value of $2.25. If there are only quarters and dimes, howmany of each kind are there?

Answer 1

Answer: We have 7 quarters and 5 dimes.

Explanation

Given

• Jeff has 12 coins

,

• Total value: $2.25.

,

• He has only quarters and dimes.

Procedure

We have to build two equations in order to find the quantity of each. Considering that q represents the quarters and d the dimes, and we have 12 coins, then we can build our first equation:

$q+d=12$

Additionally, considering that we have a total value of $2.25, a dime is 0.1 dollars and a quarter is 0.25 dollars, we can build our second equation:

$0.15q+0.1d=2.25$

If we isolate the q variable in the first equation we get:

$q=12-d$

Then, we can replace that expression of q in the second equation and simplify:

$0.25(12-d)+0.1d=2.25$$3-0.25d+0.1d=2.25$$3-0.15d=2.25$$0.15d=3-2.25$$d=\frac{0.75}{0.15}$$d=5$

Finally, we replace this value in the isolated expression of q:

$q=12-d=12-5=7$