#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?

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

Part 17) Kenji received 144 stickers

Step-by-step 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

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answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints