A charity organization is collecting change to raise money. They have collected twice as many dimes as quarters, 5 more nickels than dimes, and three times as many pennies as nickels. Make sure you answer EACH part listed below to earn the full points
1. Let x represent the number of quarters. Write an expression to represent the number of dimes.
2. Write an expression to represent the number of nickels.
3. Write an expression to represent the number of pennies.
4. If they have collected a total of 1,120 coins, how many of each coin have they collected? Show your work.
1. The expression to represent the number of dimes is 2x.
2. The expression to represent the number of nickels is 2x + 5.
3. The expression to represent the number of pennies is 3(2x + 5) or 6x + 15.
4. To find how many of each coin they have collected, we can set up an equation using the total number of coins - 1,120.
x (quarters) + 2x (dimes) + (2x + 5) (nickels) + (6x + 15) (pennies) = 1,120
Combine like terms:
x + 2x + 2x + 5 + 6x + 15 = 1,120
11x + 20 = 1,120
Now, subtract 20 from both sides:
11x = 1,100
Finally, divide by 11:
x = 100
So there are 100 quarters. Now we can use the expressions from parts 1-3 to find the other coins:
Dimes: 2x = 2(100) = 200 dimes
Nickels: 2x + 5 = 2(100) + 5 = 205 nickels
Pennies: 6x + 15 = 6(100) + 15 = 615 pennies
They have collected 100 quarters, 200 dimes, 205 nickels, and 615 pennies.