Question

Mr.Scruggs got some money for his birthday.HE SPENT 1/5OF IT ON DOG TREATS. THEN, HE DIVIDED THE REMAINDER EQUALLY AMONG HIS 3 FAVORITE CHARITIES . WHAT FRACTION OF HIS MONEY DID EACH CHARITY RECIEIVE? IF HE DONATED $60 TO EACH CHARITY , HOW MUCH MONEY DID HE RECEIVE FOR HIS BIRTHDAY?

Answer 1

I wasn't going to click on this entry, but the ALL-CAPS entranced me and enthralled me, so I had to click it.


well, if he gave his dog 1/5 of the money, what's left is just 4/5, recall 5/5 is a whole, so
`\bf \cfrac{4}{5}+\cfrac{1}{5}\implies \cfrac{5}{5}\implies 1whole`

now, let's divide that 4/5 in 3 even pieces


`\bf \cfrac{(4)/(5)}{3}\implies \cfrac{(4)/(5)}{(3)/(1)}\implies \cfrac{4}{5}\cdot \cfrac{1}{3}\implies \cfrac{4\cdot 1}{5\cdot 3}\implies \cfrac{4}{15}`

now, his donation to each charity was 60 bucks, so 4/5, of say "x", "x" being to total amount, is 60, thus (4/5)x = 60


`\bf \cfrac{4}{5}x=60\implies \cfrac{4x}{5}=60\implies x=\cfrac{5\cdot 60}{4}`

and surely you know how much that is.

Answer 2

Mr.Scruggs received $225 on his birthday.

Explanation:

Amount donated to each charity = $60

So, amount donated to 3 charities =
`60*3=180` dollars

Let the amount received on the birthday be = x

Given is that he spent 1/5 of x on dog treats, and remaining was divided among charities.

The equation can be formed as:

`x-x/5=180`

`(5x-x)/5=180`

`4x/5=180`

`4x=900`

x = 225

Hence, he received $225 on his birthday.

And to know how much each charity received, we get
`(60)/(225)`

Dividing by 5:

`(12)/(45)`

Dividing by 3:

`(4)/(15)`

Hence, each charity received
`(4)/(15)` of his money.

`(4)/(15)` of $225 is $60.