a news carrier has $7.00 in change he has 8 more quarters than dimes and five times as many nickels than quarters.how many coins of each type does he have ?
q = d+8
n = 5q
5n+10d+25q = 700
Now just plug and play!
let's start with dimes ---- x
then quarters ---- x+8
nickels ------- 5(x+8)
now to the VALUE of these
10x + 25(x+8) + 5(5)(x+8) = 700
10x + 25x + 200 + 25x + 200 = 700
60x = 300
x = 5
so
5 dimes
13 quarters
65 nickels
check:
5(10) + 13(25) + 65(5) = 700
my answer is correct
To solve this problem, let's work step by step to determine the number of each type of coin the news carrier has.
1. Let's start by assigning variables to represent the number of each coin:
- Let x be the number of dimes.
- Therefore, the number of quarters would be x + 8 (since there are 8 more quarters than dimes).
- The number of nickels would be 5 * (x + 8) (since there are five times as many nickels as quarters).
2. Now, let's calculate the total value of all the coins:
- Dimes are worth $0.10 each, so the value of dimes is 0.10x.
- Quarters are worth $0.25 each, so the value of quarters is 0.25 * (x + 8).
- Nickels are worth $0.05 each, so the value of nickels is 0.05 * 5 * (x + 8).
3. Since the news carrier has $7.00 in total, we can set up the equation:
0.10x + 0.25 * (x + 8) + 0.05 * 5 * (x + 8) = 7.00
4. Solving the equation:
0.10x + 0.25x + 2 + 0.25x + 2 = 7.00
0.60x + 4 = 7.00
0.60x = 3.00
x = 5
5. Now that we know the number of dimes (x = 5), we can calculate the number of quarters and nickels:
- Number of quarters = x + 8 = 5 + 8 = 13
- Number of nickels = 5 * (x + 8) = 5 * (5 + 8) = 65
Therefore, the news carrier has 5 dimes, 13 quarters, and 65 nickels.