Question

If `7` apples cost `y` cents, how many can you buy for `x` dollars?

(a) `(7y)/x`; (b) `(7x)/y`; (c) `(700y)/x`; (d) `(700x)/y`.

Answer 1

(d) i.e. `(700x)/y`.

Explanation:

As `y` cents buy `7` apples, `y` dollars will by `7xx100` apples.

Hence one dollar will buy `7xx100/y=700/y` apples and

`x` dollars will buy `700/y xx x` apples or `700x/y` apples.

Hence answer is (d).

Answer 2

`(700x)/y` apples

option d

Explanation:

If you find it difficult to work with variables, make an easy example first. Once you know what you did with the numbers, do the same with the variables.

If 5 apples cost 50 cents, how many can you buy for 3 dollars?

One apple costs `50 div 5 = 10` cents

`$3 = 3 xx100 = 300` cents

With `300` cents, I can buy `300 div 10 = 30` apples

What did we do?

Cents divided by the number of apples told us the cost of `1` apple.
Change dollars to cents
Divide by the cost of `1` apple:

In one step: `3xx100 div (50 div 5)`

= `300 div 50/5`

`=300 xx5/50`

`=30` apples

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If `7` apples cost `y` cents, one apple costs `y div 7` cents

`$x = x xx 100 = 100x` cents

With `100x` cents, I can buy `100x div (y div 7)`

`= 100x div y/7`

`=100x xx 7/y`

#=(700x)/y # apples