Question

If x and y are in direct proportion and y is 35 when x is 7, find y when x is 6.

Answer 1

y = 30 when x = 6

Explanation:

`(35)/(7) = (y)/(6) \\(35*6)/7 = y\\\\y = 30`

Answer 2

y is 30 when x is 6.

Explanation:

Pre-Solving

We are given that x and y are in direct proportion. This means if x increases, then y will increase, and if x decreases, y will also decrease.

A directly proportional relationship is written as
`(x_1)/(y_1) = (x_2)/(y_2)`. The ratios should equal the same amount.

We also know that when x is 7, y is 35. The question wants us to find y when x is 6.

Solving

Since we already know that when x is 7, y is 35, we can substitute that ratio into the equation for
`x_1` and
`y_1`.

`(7)/(35) =(x_2)/(y_2)`

Since we know that the value of x is 6 in the *other* proportion, we can substitute 6 for
`x_2`.

`(7)/(35) =(6)/(y_2)`

Now, we can solve for
`y_2`. We can start by simplifying
`(7)/(35)` to become
`(1)/(5)`.

Therefore, the equation will become:

`(1)/(5) =(6)/(y_2)`

We can cross multiply. The result will be:

`y_2=30`

This means that when x is 6, y will be 30.