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Answer on Algebra Question for Rachel Robinson

Question #5156
Six friends (Anita, Bill, Catherine, Diana, Evan and Fred) go to a bookstore. Each friend is given a coupon for a certain percentage off the price of one book.
a. Anita notices that the sum of the percents off listed on the six coupons is 100.
b. Bill notices that his coupon and Anita’s coupon list the same percent off.
c. Catherine points out that her percent off is the same as Diana’s and that Bill’s percent off is three times the size of Diana’s
d. Evan is happy with his 28% off coupon.
e. Fred is even happier since his coupon’s percent off is 10 times that of Diana’s coupon.

What percent off does Anita’s coupon give? Explain your answer clearly.
Expert's answer
Six friends (Anita, Bill, Catherine, Diana, Evan andFred) go to a bookstore. Each friend is given a coupon for a certain percentage
off the price of one book.
Let Anyas coupon is A, Bill’s –B…
a. Anita notices that the sum of the percents offlisted on the six coupons is 100.
A+B+C+D+E+F=100
b. Bill noticesthat his coupon and Anita’s coupon list the same percent off.
A=B
c. Catherinepoints out that her percent off is the same as Diana’s and that Bill’s percent
off is three times the size of Diana’s
C=D
B=3D
d. Evan is happy with his 28% off coupon.
E=28
e. Fred is even happier since his coupon’s percent offis 10 times that of Diana’s coupon.
F=10D
What percent off does Anita’s coupon give? Explainyour answer clearly.

S0
A+B+C+D+E+F=100
A=B
B=3D so A=3D
C=D
E=28
F=10D

3D+3D+D+D+28+10D=100
D=4 percents
A=3D=12

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