Question

Please help!!! (algebra)
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. What is the numerator of the fraction?

Answer 1

thanks for stopping by! can you help me?

Answer 2

Let n=numerator and d=denominator
a) (n+3)/d=3/4
b) n/(d+7)=1
b) n=d+7
a) (d+7+3)/d=3/4 substitute d+7 for n.
a) (d+10)/d=3/4

Answer 3

a) 4(d+10)=3d multiply each side by 4d
a) 4d+40=3d
d=-40
b) n=-40+7
n=-33
.

Answer 4

ok.

Answer 5

Okay thank you, seiga!

Answer 6

np.

Answer 7

@seiga Check the question again, the denominator is decreased by 7 NOT increased

So we have : \(\large{\frac{n}{d-7} = 1}\)

n = d-7

d = n + 7 ----------(1)

Answer 8

i see...

Answer 9

Now... since \(\large{\frac{n+3}{d} = \frac{3}{4}}\)

\(\large{4(n+3) = 3d}\)
\(\large{4n+12 = 3d}\)
Put d = n+7

4n + 12 = 3(n+7)

4n+ 12 = 3n +21

n = 9

So we have numerator = 9 and d = n + 7 = 16

hence numerator = 9 and denominator = 16

Answer 10

Got it now @scienceQs ?

Answer 11

yes! thank you =)