Question

Solve the proportion 35 over 28 equals x over 4. What is the value of x?

Answer 1

`x=5`

Explanation:

`35/28=x/4`
This is a ratio statement. The most common way to solve this is to use cross multiplication. I'll show you how to solve it that way (it's just a shortcut), but first I'll go through it step-by-step

First, our goal is to get rid of the denominators.
`cancel(28)*35/cancel(28)=x/4*28`
That's one denominatro cleared, now on to the next one:
`4*35=(28x)/cancel(4)*cancel(4)`
`4*35=28x` or `140=28x`

Now we need to isolate the `x`, so we just need to divide by `28` on both sides
`140/28=(cancel(28)x)/cancel(28)`
That simplifies to `5=x`

Now, to solve the same problem using cross multiplication, we begin with `35/28=x/4`. We just multiply the numerators (`35` and `x`) by `4` and `28` respectively, and then we divide by `28`.

It looks like this:
`35*4=28*x`
`(35*4)/28=x`
`140/28=x`
`5=x`

It just means skipping steps, but as long as you know what steps you're brushing over, you should be fine.

Answer 2

See the entire solution process below:

Explanation:

First, we can rewrite this written expression as:

`35/28 = x/4`

Now, multiply each side of the equation by `color(red)(4)` to solve for `x` while keeping the equation balanced:

`color(red)(4) xx 35/28 = color(red)(4) xx x/4`

`cancel(color(red)(4)) xx 35/(color(red)(cancel(color(black)(28))) 7) = cancel(color(red)(4)) xx x/color(red)(cancel(color(black)(4)))`

`35/7 = x`

`5 = x`

`x = 5`