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#.

2 Answers
Jun 4, 2016

(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).

Aug 22, 2017

#(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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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