Question

A number n is multiplied by 5/8 . The product is subtracted from 2/3 . The result is 7/12 . What is n?
a. 2/15
b. 6/7
c. 5/12
d. 9/17

Answer 1

a number \(n\) is multiplied by \(\frac{5}{8}\) which will give \(\frac{5}{8}n\)

Answer 2

it is then subtracted from \(\frac{2}{3}\) giving \[\frac{2}{3}-\frac{5}{8}n\]

Answer 3

the answer is given to be \(\frac{7}{12}\) telling you that
\[\frac{2}{3}-\frac{5}{8}n=\frac{7}{12}\] and your job is to solve for \(n\)
do you know how to do it?

Answer 4

Not really. Lol

Answer 5

Can you explain?

Answer 6

well, if you dislike fractions like i do, then the best thing to do is multiply both sides by the least common multiple of 3, 8 and 12, which is 24
what this really amounts to is cancelling common factors

Answer 7

if you do not dislike fractions you can work with them and solve in essentially two steps
what is your preference?

Answer 8

I don't like fractions

Answer 9

ok then lets multiply both sides by 24 first to get rid of them
start with
\[24\left(\frac{2}{3}-\frac{5}{8}n\right)=\frac{7}{12}\]

Answer 10

i meant start with
\[24\left(\frac{2}{3}-\frac{5}{8}n\right)=24\times \frac{7}{12}\]

Answer 11

on the right hand side, 12 goes in to 24 two times, so you get \(14\)\[24\left(\frac{2}{3}-\frac{5}{8}n\right)=14\]

Answer 12

no fraction on the right

Answer 13

on the left hand side, 3 goes in to 24 eight times, and eight times 2 is 16
also 8 goes in to 24 three times, and three times 5 is 15 this give you
\[16-15n=14\]

Answer 14

subtract 16 from both sides?

Answer 15

now you can solve in two easy steps
subtract 16 from both sides
right

Answer 16

so. youd get -15n= -2

Answer 17

yes

Answer 18

final step: divide both sides by \(-15\)

Answer 19

=7.5

Answer 20

or 75.

Answer 21

no, you divided upside down

Answer 22

you have \(-15n=-2\) divide by \(-15\)

Answer 23

decimal?

Answer 24

you should get \[n=\frac{2}{15}\] not \(n=\frac{15}{2}\)

Answer 25

well, i think given your answer choices you should eschew decimals and just write \(\frac{2}{15}\)

Answer 26

okay. thanks

Answer 27

yw