## anonymous one year ago i need some help on proportions

1. anonymous

If 2 over 3 ton of gravel covers 3 over 4 of a driveway, how many tons of gravel are required to cover the entire driveway?

2. SolomonZelman

it depends on the driveway length

3. anonymous

4. SolomonZelman

Are you given the length of the driveway?

5. anonymous

no

6. SolomonZelman

Oh, no need for this length..... t- ton of gravel d-driveway $$\large\color{black}{ \displaystyle \frac{2}{3}t=\frac{3}{4}d }$$

7. SolomonZelman

So, you need to solve for d.

8. anonymous

yes that is correct

9. SolomonZelman

(multiply both sides times 4/3) $$\large\color{black}{ \displaystyle \frac{2}{3}t\color{red}{\times \frac{4}{3}}=\frac{3}{4}d\color{red}{\times \frac{4}{3}} }$$

10. anonymous

idk how but your supost to do it with proportions

11. anonymous

ok i get it

12. SolomonZelman

13. anonymous

idk honestly im lost but i can multiply fractions but itll take me a sec

14. anonymous

idk i got 1 1/3 and 1

15. SolomonZelman

$$\large\color{black}{ \displaystyle \frac{2}{3}t=\frac{3}{4}d }$$ in this proportion, t is tons of gravel, and d is the driveway. $$\large\color{black}{ \displaystyle \frac{2}{3}t\color{red}{\times \frac{4}{3}}=\frac{3}{4}d\color{red}{\times \frac{4}{3}} }$$ i multiplied times 4/3 to isolate the d (the driveway), because you have to find the number of tons of gravel per a driveway. $$\large\color{black}{ \displaystyle \frac{2}{3}t\color{red}{\times \frac{ 4}{3}}=\frac{\cancel3}{\bcancel4}d\color{red}{\times \frac{\bcancel 4}{\cancel3}} }$$ 4's and 3's cancel. $$\large\color{black}{ \displaystyle \frac{2}{3}t\color{red}{\times \frac{ 4}{3}}=d }$$ and then multiply the fractions $$\large\color{black}{ \displaystyle \frac{2}{3}\times \frac{ 4}{3} \times t=d }$$ $$\large\color{black}{ \displaystyle \frac{2\times4}{3\times3}t=d }$$

16. SolomonZelman

and then what do you get? (how many tons of gravel, t, do you need, in order to cover the driveway, d?)

17. anonymous

8/6 or 1 1/3

18. SolomonZelman

3×3=9, (not 6)

19. SolomonZelman

so it is 8/9

20. anonymous

21. anonymous

ya lol

22. SolomonZelman

so you need 8/9ths tons of gravel to cover a driveway

23. SolomonZelman

yw.

24. anonymous

can you help me with one more