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# help me

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Nell and David each have some money. If Nell gives David \$16, both of

them will have the same amount of money. If David gives Nell \$9, the

amount of money Nell has to the amount of money David has will be in

the ratio 6:1. How much money do the two boys have in all?

Jan 12, 2022

#1
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How much money do the two boys have in all?

Hello Ticon!

\(n-16\ \$=d+16\ \$\\ n=d+32\ \$\\ (d-9\ \$):(n+9\ \$)=1:6\\ 6d-54\ \$=n+9\ \$\\ 6d-54\ \$=d+32\ \$+9\ \$\\ 5d=95\ \$\)

\(d=19\ \$\\ n=51\ \$\\ n+d=70\ \$\) !

Jan 13, 2022
#2
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Let the amount of money Nell have = N,

And the amount of money David have = D

Nell         David

Initiallly          N             D

Case 1          N - 16      D + 16

Case 2          N + 9       D - 9

Case 1 --> When Nell gives David \$16,

Then both have the same amount.

So, N - 16 = D + 16

N = D + 16 + 16 = D + 32

Case 2 --> When David gives Nell \$9,

Nell and David's amount will be in

The ratio 6:1.

(N + 9)/D - 9 = 6/1

N + 9 = 6D - 54

N = 6D - 63

After equating the equations from both cases,

We will get          N => D + 32 = 6D - 63

32 + 63 = 6D - D

95 = 5D

D = 95/5 = \$19

And, N = D + 32
Nell have \$51 and David have

\$19. Together they have \$(51 + 19)

= \$70

Jan 14, 2022
edited by Slimesewer  Jan 14, 2022