Question

How do you use cross products to solve `3/x=4/28`?

Answer 1

`x=21`

Explanation:

`color(blue)(3)/color(red)(x)=color(red)(4)/color(blue)(28)`

Now multiply the `color(red)"values in red"` together, the `color(blue)"values in blue"` together and equate them.

As you can see, this multiplication forms a cross (X) hence the reason it is called cross products.

`rArrcolor(red)(4x)=(color(blue)(3)xxcolor(blue)(28))`

`rArr4x=84`

To solve for x, divide both sides by 4

`(cancel(4) x)/cancel(4)=84/4`

`rArrx=21`

`color(blue)"As a check"`

substitute this value into the equation and if the left side equals the right side for this value then it is the solution.

`"left side "=3/21=cancel(3)^1/cancel(21)^7=1/7`

`"right side "=4/28=cancel(4)^1/cancel(28)^7=1/7`

`rArrx=21" is the solution"`

Answer 2

`x=21`

Explanation:

`3/x = 4/28`

`3/x = 1/7`

Cross multiply:

`x xx1 = 3xx7`

`x=21`