Joseph F. answered • 02/18/20

Mechanical Engineer with an aptitude for mathematics and physics

We have two unknowns, the number of quarters, Q and the number of dimes, D.

Since we have two unknowns, we need to come up with two equations using these unknowns

1st Equation) We know that 1 quarter = 0.25 dollars, 1 dime = 0.10 dollars and that Adriana has 16 dollars:

0.25 *Q + 0.10 * D = 16 dollars

2nd Equation) The problem also states that Adriana has two and half (2.5) times as many dimes than quarters:

D =2.5 * Q

Substitute Equation 2 into Equation 1 and solve for Q, the number of quarters

0.25 * Q + 0.10 * (2.5 * Q) = 16.00

(0.25 + 0.25) Q = 16

0.5 * Q = 16

Q = 16 / 0.5 = 32

Adriana has 32 quarters.

Adriana also she 2.5 * 32 dimes, which means she has 80 dimes

Check the results

0.25 * 32 + 0.10 *80 = 16.00

8.00 + 8.00 = 16.00

16.00 = 16.00

Liam L.

Thanks, that was a very great explanation.02/18/20