Question 1 :
Before a big test, James memorized 10 percent more words than Zach. Zach memorized 30 percent more words than Amy. If Amy memorized a words, how many words did James memorize in terms of a?
Question 2 :
Call center A handles 20% fewer calls than Call center B. Call center B handles 20% fewer calls than Call center C. If Call center A handles 1,200 calls, how many calls does Call center C handle?
Question 3 :
If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?
Question 4 :
The price of a text book this year is 20% greater than the price last year. If this year's price is p, what was last year's price in terms of p?
Question 5 :
A cylinder has a base radius of r and a height of h. If the radius is reduced by 30%, how would the volume of the cylinder change?
1. Answer :
Given : Amy memorized a words and Zach memorized 30 percent more words than Amy.
Number of words memorized by Zach :
= (100 + 30)% of a
= 130% of a
= (1.30)a
Given : James memorized 10 percent more words than Zach.
Number of words memorized by James :
= (100 + 10)% of (1.30)a
= 110% of (1.30)a
= (1.10)(1.30)a
2. Answer :
Call center A handles 20% fewer calls than Call center B. Call center B handles 20% fewer calls than Call center C. If Call center A handles 1,200 calls, how many calls does Call center C handle?
Let x be the number of calls handles by Call center C.
Given : Call center B handles 20% fewer calls than Call center C.
Number of calls handled by Call center B :
= (100 - 20)% of x
= 80% of x
= 0.8x
Given : Call center A handles 20% fewer calls than Call center B.
Number of calls handled by Call center A :
= (100 - 20)% of 0.8x
= 80% of 0.8x
= (0.8)(0.8x)
= 0.64x
Given : Call center A handles 1200 calls.
0.64x = 1200
Divide both sides by 0.64.
x = 1875
Call center C handles 1875 calls.
3. Answer :
If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?
Given : X is 20% of Y.
X = 0.2Y
Divide both sides by 0.2.
5X = Y
Given : Y is 30% of Z.
Y = 0.3Z
Substitute Y = 5X.
5X = 0.3Z
Divide both sides by 5.
X = 0.06Z
X = (6/100)Z
X = 6% of Z
6% of Z is X.
4. Answer :
Let x be the price of the text book last year.
Given : The price of a text book this year is 20% greater than the price last year.
This year's price = (100 + 20)% of x
= 120% of x
= 1.2x
Given : This year's price is p
1.2x = p
Divide both sides by 1.2.
x = (1/1.2)p
x = (10/12)p
x = (5/6)p
5. Answer :
Volume of a cylinder base radius of r and a height of h :
= πr^{2}h
If the radius is decreased by 30%, then the new radius is
= (100 - 30)% of r
= 70% of r
= 0.7r
Volume of the cylinder after the radius is reduced by 30% :
= π(0.7r)^{2}h
= π(0.49r^{2})h
= 0.49(πr^{2}h)
= (49/100)(πr^{2}h)
= 49% of (πr^{2}h)
100 - 49 = 51
Volume of the cylinder would decrease by 51%.
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