Question

A glass is 4/7 full. Then 70 cm³ orange juice is poured in. The glass is now 3/4 full.

Answer 1

Answer:

392cm^2.

Step-by-step explanation:

to do this, we must find a common denominator of the two, which is fairly simple- just multiply the denominators by each other, then the numerators of each fraction by the denominator of the other to change the numerator.

This changes 4/7 to 16/28 full and 3/4 to 21/28 full. Now we can move on to the real math-

We can take 21/28 and subtract 16/28 to get how much of the glass the 70cm^3 takes up.

We now have 5/28 of the glass accounting for 70 cm ^3 of liquid. Now from here, we can take 70/ 5 to find what 1/28 of the glass equals.

we get 14 cm ^3 of liquid per 28th of glass.

now multiply 14cm^3 by 28 to get the total volume of the glass.

14*28=392

Therefore, the total volume of the glass is 392cm^2.

Answer 2

Answer:

The volume of the glass is 217.8 cm³

Step-by-step explanation:

If the glass were initially 4/7 full, that means 3/7 of the volume is still available to hold more juice.

Let v represent the volume of the glass.  

Then (3/7)v + 70 cm³ = (3/4)v.

We need to solve this for v.

Here the LCD is 28.  Thus,

(3/7)v + 70 cm³ = (3/4)v →  (12/28)v + 70 cm³ = (21/28)v.

Subtracting  (12/28)v from both sides, we get:

70 cm³ = (9/28)v.

We can isolate v by mult. both sides by the inverse of 9/28, which is 28/9:

(28/9)(70 cm³) = v

The volume of the glass is 217.8 cm³