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
b) use you defines variable to write algebraic expressions to represent the number of quarters,dime.nickels,and pennies collected.
d = 2 q
n = d + 22
p = 3 n
end of what you asked
Now you did not ask but the number of cents collected is
p + 5 n + 10 d + 25 q
put all in terms of pennies p
n = p/3
d = p/3 - 22
q = 2/2 = p/6 - 11
so
total cents = p + 5p/3 + 10p/3-220 +25 p/6 - 275
= 61 (p/6) - 250
Let's define the variables as follows:
Let x = the number of quarters collected.
Since the number of dimes collected is twice as many as quarters, we can express it as 2x.
Since the number of nickels collected is 22 more than dimes, we can express it as 2x + 22.
Since the number of pennies collected is three times as many as nickels, we can express it as 3(2x + 22).
Let's define the variables:
Let q represent the number of quarters collected.
Let d represent the number of dimes collected.
Let n represent the number of nickels collected.
Let p represent the number of pennies collected.
Now, let's write algebraic expressions to represent the number of quarters, dimes, nickels, and pennies collected based on the given information:
1) "They have collected twice as many dimes as quarters":
Since they have collected twice as many dimes as quarters, we can express the number of dimes collected as 2q.
2) "22 more nickels than dimes":
Since there are 22 more nickels than dimes, we can express the number of nickels collected as d + 22.
3) "3 times as many pennies as nickels":
Since there are 3 times as many pennies as nickels, we can express the number of pennies collected as 3n.
Therefore, the algebraic expressions for the number of quarters, dimes, nickels, and pennies collected are:
q for quarters,
2q for dimes,
d + 22 for nickels,
3n for pennies.