If it takes 4/7 of a ton of concrete to complete 7/8 of bridge, how much is needed to complete the entire bridge

Question

joshtray · Answer

If 4/7 of a ton is needed to complete 7/8 of a bridge, 1/8 of a bridge will need 4/7 X 1/7
which is 4/49 tons of concrete will be used. So to complete 8/8 which is the whole bridge, you will need 4/49 X 8 which is 32/49 of a ton of concrete

joshtray · Answer

If you dont understand I could explain more

jessicaprieto · Answer

If you can break it down for me that would be great.

calculusxy · Answer

$$\large \frac{\frac{4}{7} \text{ }\text{ton}}{\frac{7}{8} \text{ } \text{of a bridge}} = \frac{x}{1}$$

calculusxy · Answer

Making a proportion and trying to solve for x would be useful.

mathstudent55 · Answer

You can also use a proportion.
x is the amount needed for the entire bridge.

4/7 ton is to 7/8 bridge as x is to 1 bridge

$\large \dfrac{\frac{4}{7}}{\frac{7}{8}} = \dfrac{x}{1} $

Cross multiply:

$\dfrac{7}{8}x = \dfrac{4}{7} \times 1$

$\dfrac{7}{8}x = \dfrac{4}{7} $

You have $\dfrac{7}{8}x$, and you want x, so multiply both sides by the reciprocal of the fraction

$\dfrac{8}{7} \times \dfrac{7}{8}x = \dfrac{8}{7} \times \dfrac{4}{7} $

$x = \dfrac{32}{49} $

Answer: $\dfrac{32}{49}$ of a ton is needed to complete the entire bridge

joshtray · Answer

Sorry I was quite busy

joshtray · Answer

But their explanation is correct

jessicaprieto · Answer

No problem - This makes it very simple.  Thank you very much