Question

The variables y and x have a proportional relationship, and y = 5 when x = 4.

What is the value of x when y = 8?

Answer 1

`\boxed{a = 6.4}`

Explanation:

Given:

`x:y = (4):(5)`

Let the value of "x" be known as "a".

`x:y = a:8`

Setting up the proportion:

`\rightarrow 4:5 = a :8`

Multiplying the middles and the extremes:

`\rightarrow 5a = 4 * 8`

Simplifying the RHS:

`\rightarrow a = (4 * 8)/(5)`

`\rightarrow \boxed{a = 6.4}`

Thus, the value of x is 6.4 when y is 8.

Answer 2

`\sf x=(32)/(5)`

(or x = 6.4 if you want it in decimal form)

Explanation:

If y and x have a proportional relationship, then:

• y = kx (for some constant k)

Given:

• x = 4
• y = 5

Substitute the given values into the equation to find k:

⇒ 5 = k(4)

⇒ k = 5/4

Therefore,
`\sf y=\frac54x`

When y = 8, substitute y = 8 into the equation and solve for x:

`\sf \implies \frac54x=8`

`\sf \implies x=8 \cdot \frac45`

`\sf \implies x=(32)/(5)`