SOLUTION: Hi Henry spent $380 on clothes and $170 on food and gave 40% of the remainder to Janet. Then he saved the rest of his money. If he saved 30% of his original sum of money, how muc

Question 1170708: Hi
Henry spent $380 on clothes and $170 on food and gave 40% of the remainder to Janet. Then he saved the rest of his money. If he saved 30% of his original sum of money, how much did he give janet
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = his original sum of money.
he spent 380 + 170 = 550 on food and clothes.
that means he had (x - 550) left.
he gave 40% of this to janet.
that means he had (x - 550) - .4 * (x - 550) left.
simplify this to get that he had x - 550 - .4 * x + 220 left.
combine like terms to get that he had .6 * x - 330 left.
this was 30% of his original money which means that x = (.6 * x - 330) / .3
simplify this to get x = 2 * x - 1100
solve for x to get x = 1100

original amount of money that he had was 1100.
confirm by replacing x in the original equation to get:
1100 - 550 = 550 left.
550 - .4 * 550 = 330 left.
330/.3 = 1100.

the numbers are good.
you are asked how much he gave to janet.
he gave janet 40% of 550 = 220.
that's your solution.

RELATED QUESTIONS
Hi henry spent 550 dollars on food and clothes and gave 40% of the remainder to janet.... (answered by josmiceli,TeachMath)

Every month. Andie spent 1/5 of his salary on food and 2/3 of the remaining salary on... (answered by greenestamps,ikleyn,MathTherapy)

Hi Jenny saved 360 dollars of her monthly income and spent 1/6 of the rest on food.... (answered by ankor@dixie-net.com)

Hi Sarah spent 3/8 of her allowance on food and 1/3 of the remainder on clothes. Then... (answered by josgarithmetic,mananth,MathTherapy,greenestamps,Edwin McCravy,ikleyn,AnlytcPhil)

Hi joanne and alex had some money.joanne gave 1/4 of her money to her mom.she then saved (answered by ankor@dixie-net.com)

Hi in January joyce kept 80 percent of her salary of which she then gave 1/5 to her mum... (answered by greenestamps)

Raj spent 25% of his money on clothes and 1/3 of the remainder on food. After giving $441 (answered by math_tutor2020)

Last month, Alex spent 40% of his salary on a laptop. He then spent 30% of it on his... (answered by oberobic)

Hi Jayden gave 3/10 of his salary to his mother and spent 15/49 of the remainder on a... (answered by mananth)