SOLUTION: Hi henry has 25% more money than angie.catherine has 20 percent more than henry.if catherine gives 90 dollars to angie all of them would have an equal amount. How much do they hav

Question 1034299: Hi
henry has 25% more money than angie.catherine has 20 percent more than henry.if catherine gives 90 dollars to angie all of them would have an equal amount. How much do they have altogether.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let h = the amount of money that henry has.
let c = the amount of money that catherine has.
let a = the amount of money that angie has.

you are given:

h = 1.25 * a
c = 1.20 * a

if catherine gives 90 dollars to angie, then they will all have the same amount of money.

c - 90 = a + 90

after the exchange of money, you get:

h = c - 90
h = a + 90

you were already given that h = 1.25 * a.

h = a + 90 becomes 1.25 * a = a + 90.

subtract a from both sides of the equation to get .25 * a = 90

solve for a to get a = 360

this means that a + 90 = 450.

a + 90 = h means that h = 450.

c - 90 = a + 90 means that c - 90 = 450 which means that c = 540.

so, ........

you start with:

h = 450
a = 360
c = 540.

subtract 90 from c to get c - 90 = 450.
add 90 to a to get a + 90 = 450.
h is already equal to 450 and hasn't changed.

they're all equal after you took 90 from catherine and gave it to angie.

altogether they have 3 * 450 = 1350.

their original sum should be the same.
450 + 360 + 540 = 1350.

everything checks out.

the sum of their money is 1350.

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