A charity organization is collecting change to raise monay. They have collected twice as many dimes as quarters, 22 more nickels than dimes, and 3 times as many pennies as nickels.
a) define a variable for the number of quarters collected.
b) use you defines variable to write algebraic expressions to represent the number of quarters,dime.nickels,and pennies collected.
c)if they have collected a total of 2134 coins, how much many of each coin have they collected?
someone please help me????
a) Let's define the variable "q" as the number of quarters collected.
b) Based on the given information, we can write the following algebraic expressions for the number of each coin collected:
- Quarters: q
- Dimes: 2q (twice as many as quarters)
- Nickels: 2q + 22 (22 more than dimes)
- Pennies: 3(2q + 22) (3 times as many as nickels)
c) To solve for the number of each coin collected, we can set up an equation based on the total number of coins collected:
q + 2q + (2q + 22) + 3(2q + 22) = 2134
Simplifying the equation:
q + 2q + 2q + 22 + 6q + 66 = 2134
Collecting like terms:
11q + 88 = 2134
Subtracting 88 from both sides:
11q = 2046
Dividing both sides by 11:
q = 186
Therefore, they have collected 186 quarters.
Using the algebraic expressions from part b:
- Dimes: 2q = 2 * 186 = 372 dimes
- Nickels: 2q + 22 = 2 * 186 + 22 = 394 nickels
- Pennies: 3(2q + 22) = 3 * (2 * 186 + 22) = 1776 pennies