Question

If x and y are in direct proportion and y is 42 when x is 6, find y when x is 11

Answer 1

Hi there!

We are asked to find y when x is 11, when we're given some clues.

We know that x and y are directly proportional to each other. So, we can write it as:

• y = kx, where k is the constant of proportionality

First we should find k. So we know that y = 42 when x = 6, and we substitute that into the equation to find k:

`\sf{42=k*6}`

`\sf{42=6k}`

Divide both sides by 6:

`\sf{7=k}`

Now that we know what the constant of proportionality is, we can find y. The problem also told us that x = 11.

So now we have two values: k = 7, x = 11.

y = kx

y = 7 * 11

y = 77

Therefore, y = 77.

To summarise, if y varies directly with x (when y is directly proportional to x and vice versa) as y = kx, where k = constant of proportionality.

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Best wishes!

Answer 2

y = 77

Explanation:

Certainly! To solve the problem simply:

The ratio
`\(x:y\) is \(6:42\)`, which simplifies to
`\(1:7\)`

When
`\(x\) is 11, \(y\)` can be found by multiplying 11 by 7 (since the ratio is 1:7).

`\(y = 11 * 7 = 77\)`

So, when
`\(x\) is 11, \(y\) is 77.`