Question

A glass is 1 6 full. Then 95cm3 of orange juice is poured in. The glass is now 4 5 full. What is the total volume of the glass?

Answer 1

let x = the amount of orange juice in a full glass.

the glass is 1/6 full = 1/6 * x

add 95 cubic centimeters and the glass becomes 4/5 full.

equation for that is:

1/6 * x + 95 = 4/5 * x

subtract 1/6 * x from both sides of this equation to get:

95 = 4/5 * x - 1/6 * x

multiply 4/5 * 6/6 and multiply 1/6 * 5/5 and the equation becomes:

95 = 24/30 * x - 5/30 * x

combine like terms to get 95 = 19/30 * x

multiply both sides of the equation by 30/19 to get:

30/19 * 95 = 30/19 * 19/30 * x

simplify to get:

30/19 * 95 = x

solve for x to get x = 150.

the volume of the glass is 150 cubic centimeters.

1/6 * 150 = 25

4/5 * 150 = 120

the difference between 4/5 full and 1/6 full is 95 cubic centimeters.

solution is that the volume of the glass is 150 cubic centimeters.