Question

Kirsten has 25 coins. In her collection she has dimes and quarters. If the total is $4.00. How many dimes and how many quarters does she have? Part A: Write a system of equations to express this situation. Let d= the number of dimes and q= the number of quarters. Part B: Solve the system of equations to determine the dimes and number of quarters

Answer 1

Explanation:

Because we have 2 unknowns, we need 2 equations. One equation will represent the number of coins we have, the other will represent the value of the coins, since they are definitely not the same. If we have a total of 25 coins made up of dimes and quarters:

d + q = 25

Now for the value of these, we know that a dime is worth .10 and a quarter is worth .25, and we also know that the total value of the coins we have is $4.

.10d + .25q = 4

There are the 2 equations we need. Go back to the first one and solve it for either d or q. Let's solve for d:

d = 25 - q

Now use the substitution method and sub in 25 - q for d in the other equation:

.10(25 - q) + .25q = 4 and

2.5 - .10q + .25q = 4 and

2.5 + .15q = 4 and

.15q = 1.5 so

q = 10

That means we have 10 quarters. Sub that in for q in the first equation to solve for d:

d + q = 25 and

d + 10 = 25 so

d = 15

We have 15 dimes and 10 quarters.