Question

Two jars contain sweets. Jar X has red and white sweets in the ratio 1:4, and jar Y has red and white sweets in the ratio 1:6. Two jars are then mixed together. Find the smallest number of sweets that could have been in each jar if the red and white sweets are now in these ratios
a. 1:6 b. 1:7 c. 1:8

Answer 1

Answer:

Jar X  will be empty  & Jar Y  will have 7 Sweets  in total

Step-by-step explanation:

Let say Jar X contains  = 5X

Red Sweets = X

White Sweets = 4X

Let say Jar Y contains  = 7Y

Red Sweets = Y

White Sweets = 6Y

Mixed together

Red Sweets = X + Y

White Sweets = 4X + 6Y

a : red and white sweets are in 1 : 6 Ratio

=> 6X + 6Y  = 4X + 6Y

=> 2X = 0

=> X = 0

=> Jar X  will be empty  & Jar Y  will have 7 Sweets  in total

b : red and white sweets are in 1 : 7 Ratio

=> 7X + 7Y  = 4X + 6Y

=> 3X = -Y

not Possible

c : red and white sweets are in 1 : 8 Ratio

=> 8X + 8Y  = 4X + 6Y

=> 4X = -2Y

=> 2X = - Y

not Possible