Griffindore
  • Griffindore
i need some help on proportions
Mathematics
schrodinger
  • schrodinger
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Griffindore
  • Griffindore
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?
SolomonZelman
  • SolomonZelman
it depends on the driveway length
Griffindore
  • Griffindore
idk its 7th grade math

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SolomonZelman
  • SolomonZelman
Are you given the length of the driveway?
Griffindore
  • Griffindore
no
SolomonZelman
  • SolomonZelman
Oh, no need for this length..... t- ton of gravel d-driveway \(\large\color{black}{ \displaystyle \frac{2}{3}t=\frac{3}{4}d }\)
SolomonZelman
  • SolomonZelman
So, you need to solve for d.
Griffindore
  • Griffindore
yes that is correct
SolomonZelman
  • SolomonZelman
(multiply both sides times 4/3) \(\large\color{black}{ \displaystyle \frac{2}{3}t\color{red}{\times \frac{4}{3}}=\frac{3}{4}d\color{red}{\times \frac{4}{3}} }\)
Griffindore
  • Griffindore
idk how but your supost to do it with proportions
Griffindore
  • Griffindore
ok i get it
SolomonZelman
  • SolomonZelman
good, so what will be your answer?
Griffindore
  • Griffindore
idk honestly im lost but i can multiply fractions but itll take me a sec
Griffindore
  • Griffindore
idk i got 1 1/3 and 1
SolomonZelman
  • 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 \(\large\color{black}{ \displaystyle \frac{2}{3}\times \frac{ 4}{3} \times t=d }\) \(\large\color{black}{ \displaystyle \frac{2\times4}{3\times3}t=d }\)
SolomonZelman
  • SolomonZelman
and then what do you get? (how many tons of gravel, t, do you need, in order to cover the driveway, d?)
Griffindore
  • Griffindore
8/6 or 1 1/3
SolomonZelman
  • SolomonZelman
3×3=9, (not 6)
SolomonZelman
  • SolomonZelman
so it is 8/9
Griffindore
  • Griffindore
oh my bad so 8/9
Griffindore
  • Griffindore
ya lol
SolomonZelman
  • SolomonZelman
so you need 8/9ths tons of gravel to cover a driveway
SolomonZelman
  • SolomonZelman
yw.
Griffindore
  • Griffindore
can you help me with one more

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