Question

Dillon has saved 57 coins in his piggy bank. The coins are a mixture of quarters and dimes. He has saved $12 so far. Let q = # of quarters and d = # of dimes.

Answer 1

Answer: 42 quarters and 15 dimes.

Step-by-step explanation:

If q is the number of quarters, and d the number of dimes, we have that:

q + d = 57

q*0.25 + d*0.10 = 12

the first step is isolating one of the variables in one of the equation, it is easier to do it in the first one, let's isolate q.

q = 57 - d

now, we can replace this in the second equation and solve it for d.

q*0.25 + d*0.10 = 12

(57 - d)*0.25 + d*0.10 = 12

57*0.25 +d*(0.10 - 0.25) = 12

57*0.25 - d*0.15 = 12

-d*0.15 = 12 - 57*0.25 = -2.25

d = (-2.25)/(-0.15) = 15

So the number of dimes is 15, this means that the number of quarters must be:

q = 57 - d = 57 - 15 = 42

Answer 2

Answer:

Dillion has 42 quarters and 15 dimes.

Step-by-step explanation:

Let the number of quarters=q

Let the number of dimes=d

Dillon has saved 57 coins in his piggy bank.

Therefore:

q+d=57

Now, 1 dime=$0.10 and 1 quarter=$0.25.

We multiply the value of each coin by the number of coins present.

Since Dillion has a total of $12

Therefore:

0.1d+0.25q=12

We solve the two equations simultaneously.

From equation 1, q=57-d

Substitute q=57-d into 0.1d+0.25q=12

0.1d+0.25(57-d)=12

0.1d+14.25-0.25d=12

0.1d-0.25d=12-14.25

-0.15d=-2.25

Divide both seides by -0.15

d=15

Recall: q=57-d

          q=57-15=42

Therefore, Dillion has 42 quarters and 15 dimes.