Question

Peter & Alex share a lottery win of £4450 in the ratio 4 : 1.
Peter then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3.
How much more does his wife get over their son?

Answer 1

$\boxed {\underline {\mathbb {QUESTION:-}}}$

Peter & Alex share a lottery win of £4450 in the ratio 4 : 1. Peter then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3. How much more does his wife get over their son?

$\boxed {\underline {\mathbb {FINAL\:ANSWER:-}}}$

$\£ 1068$

$\boxed {\underline {\mathbb {GIVEN:-}}}$

• Peter & Alex share a lottery win of £4450 in the ratio 4 : 1

• Peter then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3

$\boxed {\underline {\mathbb {TO\:FIND:-}}}$

How much money his wife get over their son

$\boxed {\underline {\mathbb {THINGS\:TO\:ASSUME:-}}}$

• Let the money of lottery that peter get = 4x

• Let the money of lottery that alex  get = x

And

• Out of peter’s share amount himself get = y

• Amount his wife get = 6y

• Amount their son get =3y

$\boxed {\underline {\mathbb {SOLUTION:-}}}$

according to question

peter share + alex share =lottery

hence $\boxed {4x+x=4450}$

$4x+x=4450$

$5x=4450$ [after adding 4x and x gives 5x]

$x=\frac{4450}{5}$ [bringing 5 to RHS divides]

$x= \£ 890$

• money of lottery that peter get $= 4x \implies 890 \times 4 \implies \boxed {\£3560}$

• money of lottery that alex  get $= x \implies \boxed {\£890}$

$peter+ wife+son=peter \:share \:of\: lottery$

$y+6y+3y=3560$

$10y= 3560$  [ ←after adding y and 6y and 3y we get 10y]

$y=\frac{3560}{10}$  [ ←bringing 10 to RHS it get divide]

y=356

• amount he get for himself after getting lottery $= y \implies \boxed{356}$

• Amount his wife get $= 6y \implies 6 \times 356 \implies \boxed {\£ 2136}$

• Amount their son get $=3x \implies 3 \times 356 \implies \boxed {\£ 1068}$

Money his wife get over their son  

$=2136-1068$ [← how much money did mother get more than his son]

$\boxed{\£ 1068}$

Answer 2

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