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?
a. X Quarters.
b. 2x Dimes.
(2x+22) Nickels.
3(2x+22) Pennies.
c. X + 2x +(2x+22) + 3(2x+22)=2134.
X + 2x + 2x + 22 + 6x + 66 = 2134
11x + 88 = 2134
11x = 2046
X = 186 Quarters.
2x = 2*186 = 372 Dimes.
2x+22 = 372 + 22 = 394 Nickels.
3(2x+22) = 3 * 394 = 1182 Pennies.
What is it’s 3201
a) Let's define the variable "q" for the number of quarters collected.
b) Based on the given information, we can write the algebraic expressions for the number of each coin collected:
- Number of dimes = 2q (twice as many dimes as quarters)
- Number of nickels = 2q + 22 (22 more nickels than dimes)
- Number of pennies = 3(2q + 22) (3 times as many pennies as nickels)
c) To find the number of each coin collected, we need to solve the equation involving the total number of coins:
Total number of coins = Number of quarters + Number of dimes + Number of nickels + Number of pennies
2134 = q + 2q + 2q + 22 + 3(2q + 22)
Simplifying the equation:
2134 = q + 2q + 2q + 22 + 6q + 66
2134 = 11q + 88
Now, solve for q:
2134 - 88 = 11q
2046 = 11q
q = 186
Therefore, the number of quarters collected is 186. Substituting this value back into the algebraic expressions:
- Number of dimes = 2q = 2(186) = 372
- Number of nickels = 2q + 22 = 2(186) + 22 = 394
- Number of pennies = 3(2q + 22) = 3(394) = 1182
So the charity organization has collected 186 quarters, 372 dimes, 394 nickels, and 1182 pennies.