Question

#16 Carmen had $130 more than her sister, Rosa. Rosa had twice as much money as their youngest sister Zoe. If their mother gave Carmen $60 and Rosa $80, Carmen would have twice as much money as Rosa. What was the total amount of money they had in the beginning?

#17 Kenji, James and Ethan shared 240 stickers. Kenji received twice as many stickers as James. James received 3 times as many stickers as Ethan. How many stickers did Kenji receive?

Answer 1

Part 16) In the beginning Carmen had $160, Rosa has $30 and Zoe had $15

Part 17) Kenji received 144 stickers

Explanation:

Part 16)

Let

x -----> the total amount of money Carmen had in the beginning

y -----> the total amount of money Rosa had in the beginning

z -----> the total amount of money Zoe had in the beginning

we know that

x=y+130 -----> equation A

y=2z -----> equation B

x+60=2(y+80) -----> equation C

Substitute equation A in equation C and solve for y

(y+130)+60=2(y+80)

y+190=2y+160

2y-y=190-160

y=$30

Find the value of x

x=y+130-----------> x=30+130=$160

Find the value of z

y=2z

z=y/2

z=30/2=$15

therefore

In the beginning

Carmen had $160, Rosa has $30 and Zoe had $15

Part 17)

Let

x -----> the number of stickers received by Kenji

y -----> the number of stickers received by James

z -----> the number of stickers received by Ethan

we know that

x+y+z=240 ----> equation A

x=2y -----> equation B

y=3z ----> z=y/3 ----> equation C

substitute equation B and equation C in equation A and solve for y

(2y)+y+(y/3)=240

(10/3)y=240

y=240*3/10

y=72

Find the value of x

x=2y ----> x=2(72)=144

therefore

Kenji received 144 stickers