Ken and Ivan had some sweets. After Ken gave away 5/7 of his sweet, he had 2/3 as many sweets as Ivan. Ivan then gave away 120 sweets and he had 1/4 as many sweets as Ken. How many sweets did each of them have at first?

Ivan had 288 sweet while Ken had 672 sweets

Step-by-step explanation:

Let the number of sweets owned by Ken and Ivan be k and v respectively.

After Ken gave away 5/7 of his sweet, what he had left

= k - 5k/7

= 2k/7

he had 2/3 as many sweets as Ivan then

2k/7 = 2v/3

Divide both sides by 2 and cross multiply

7v = 3k

Ivan then gave away 120 sweets, Ivan would have

v - 120 = k/4

multiply both sides by 4

4v - 480 = k

7v = 3(4v - 480)

7v = 12v - 1440

12v - 7v = 1440

5v = 1440

v = 1440/5

= 288

7v = 3k

7 * 288 = 3k

k = 7 * 288/3

= 672

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)