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
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.
