SOLUTION: lilly and ellsa are both sister before mom gave them this month allowance lilly had $750 and Ellsa had $215 after mom gave them equal allowance lilly had twice as much as ellsa .ho

Question 1135510: lilly and ellsa are both sister before mom gave them this month allowance lilly had $750 and Ellsa had $215 after mom gave them equal allowance lilly had twice as much as ellsa .how much money did mom give them
Found 4 solutions by Theo, josgarithmetic, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
lilly had 750 and elise had 215.
their mom gave them x allowance each.
after that, lilly had twice as much as elise.

750 + x = 2 * (215 + x)
simplify to get 750 + x = 430 + 2 * x
subtract 430 from both sides of the equation and subtract x from both sides of the equation to get 750 - 430 = 2x - x
simplify to get 320 = x

the allowance was 320.

after the allowance, .....

lilly had 750 + 320 = 1070.
elise has 215 + 320 = 535.

1070 is two times 535 which means the solution is good.

solution is their mom gave them 320 each.

Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!

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Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

750 + x = 2*(215+x) 750 + x = 430 + 2x 750 - 430 = 2x - x 320 = x. Answer. The allowance value was $320. CHECK. 750 + 320 = 1070; 215 + 320 = 535. 1070 is exactly two times 535. ! Correct !

Solved.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

You have received 3 responses, all showing the same formal algebraic solution.

Solving problems like this mentally is good exercise for the brain. Here is a simple informal solution using logical reasoning and some simple arithmetic.

Lilly starts with $750 and Ellsa with $215; the difference is $535.

Their mother gives each of them the same amount, after which Lilly has twice as much as Ellsa.

Since they both received the same additional amount, the difference between their amounts is still $535.

If Lilly now has twice as much as Ellsa, and the difference between their two amounts is $535, then Ellsa has $535 and Lily has 2*$535 = $1070.

Since Lilly started with $750 and now has $1070, the amount her mother gave her was $1070-$750 = $320.
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