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?
7 pennies and 1 dime
a) Let's define a variable for the number of quarters collected. We can use 'q' to represent the number of quarters.
b) Now, let's write algebraic expressions to represent the number of quarters, dimes, nickels, and pennies collected based on the information given:
- Number of quarters: q
- Number of dimes: 2 * (number of quarters) = 2q (twice as many dimes as quarters)
- Number of nickels: 2q + 22 (22 more nickels than dimes)
- Number of pennies: 3 * (number of nickels) = 3 * (2q + 22) = 6q + 66 (three times as many pennies as nickels)
c) The total number of coins collected is given as 2134. We can now create an equation to represent the total number of coins:
q + 2q + (2q + 22) + (6q + 66) = 2134
Now, we can solve this equation to find the values of q, dimes, nickels, and pennies collected.