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 Let q = the number of quarters.

Part B:
Solve the system of equations to determine the number of dimes and the number of quarters.

Answer 1

15 dimes and 10 quarters

Explanation:

When solving problems involving money, there are 2 things that you need to pay attention to: the NUMBER of coins and the VALUE of the coins. For example, if I have 2 quarters, I have 50 cents. 2 ≠ 50. Number of coins and value of coins need to be expressed separately.

If Kirsten has a total of 25 coins that is made up of dimes and quarters, we are referring to the NUMBER of coins she has.

d + q = 25 (That says, "The number of dimes plus the number of quarters equals a total number of 25")

Now for the value part. We need an equation that satisfies the equation that says, "The value of the dimes plus the value of the quarters has a total value of $4". A dime is worth .10 and a quarter is worth .25. Putting that all together into an equation that relates the value of the coins to the total value:

.10d + .25q = 4.00

Now we have 2 equations that we can solve by substitution. Solve the first equation for, let's say, d:

If d + q = 25, then

d = 25 - q

Sub that in now for d in the second equation.

If .10d + .25q = 4.00 then

.10(25 - q) + .25q = 4.00 and, distributing,

2.5 - .10q + .25q = 4.00 and, combining like terms,

2.5 + .15q = 4.00 and, simplifying some more,

.15q = 1.5 so, dividing both sides by q,

q = 10. We have 10 quarters. Now we go back to the first equation regarding the NUMBER of coins.

If

d + q = 25, then

d + 10 = 25 and

d = 15

We have 15 dimes and 10 quarters. A total NUMBER of 25 coins with a value of $1.50 in dimes + $2.50 in quarters = $4