Question

The students Jane, Joey, and Josephine were hungry during lunch. They decided to buy a whole pizza and ate it. They contributed their money Jane R40, Joey R20, and Josephine R40. Jane bought a large pizza. They succeeded in eating the whole pizza. Jane ate twice as much as Josephine and Joey ate 1 1/2 times as much as Josephine. What part of the pizza did each student eat, show all your work and explain your thinking. ​

Answer 1

Jane ate 4/9 of the pizza, Joey ate 1/3 (or 3/9) of the pizza, and Josephine ate 2/9 of the pizza

Explanation:

Let x = the part which Jane ate

y = the part which Joey ate

z = the part which Josephine ate

now Jane ate twice as much as Josephine so,

x = 2z

also, Joey ate 1 1/2 as much as Josephine

Note: 1 1/2 = (2/2)+(1/2) = 3/2

so,

y = (3/2)z

Now,

they ate the whole pizza so,

the part that Jane ate + the part that Joey ate + the part that Josephine ate = 1 whole pizza

or,

x + y + z =1

now, we put the values of x and y into this last equation, we get,

`(2z) + (3/2)z + z = 1\\3z +(3/2)z=1\\z(3+3/2)=1\\z(9/2)=1\\\\z=2/9`

so Josephine ate 2/9 of the pizza

for Jane,

x = 2z,

x = 2(2/9)

x = 4/9

so Jane ate 4/9 of the pizza

For Joey,

y = (3/2)z

y = (3/2)(2/9)

y = 1/3

soJoey ate 1/3 of the pizza