Peter & Sam won some money in a competition. Peter won 5 times as much money as Sam. Sam won $4200 less than Peter.
a. What was the ration of the amount of money Peter won to the amount of money Sam won to the total amount of money both boys won?
b. What fraction of the total amount of money both boys won did Peter win?
c. What fraction of the total amount of money both boys won did Sam won?
d. How much money did each person win?
P = 5 S
P = S + 4200
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Now use algebra
4S = 4200
S = 1050
P = 5250
a. P:S:(P+S) = 525:105:630 = 5:1:6
b. P/(P+S) = 525/630 = 5/6
c. S/(P+S) = 1/6
d. Already answered above.
LOLZ CAT
To solve this problem, we'll need to use some algebra. Let's go through step by step to find the answers to each of the questions:
a. What was the ratio of the amount of money Peter won to the amount of money Sam won to the total amount of money both boys won?
Let's start by assigning variables to the unknowns. Let's say Peter won x amount of money and Sam won y amount of money.
According to the problem statement, Peter won 5 times as much money as Sam, so we can write the equation: x = 5y
Now, we know that Sam won $4200 less than Peter. So we can write another equation: y = x - 4200
We can substitute x from the first equation into the second equation: y = (5y) - 4200
Now we can solve for y:
4y = 4200
y = 1050
Substituting the value of y back into the first equation, we can find x:
x = 5(1050)
x = 5250
The total amount of money both boys won is x + y = 5250 + 1050 = 6300.
Therefore, the ratio of the amount of money Peter won to the amount of money Sam won to the total amount of money both boys won is:
Peter:Sam:Total = 5250:1050:6300 = 5:1:6
b. What fraction of the total amount of money both boys won did Peter win?
Peter won $5250 out of the $6300 total. To find the fraction, we divide Peter's winnings by the total amount:
Fraction = 5250/6300 = 5/6.
c. What fraction of the total amount of money both boys won did Sam win?
Sam won $1050 out of the $6300 total. To find the fraction, we divide Sam's winnings by the total amount:
Fraction = 1050/6300 = 1/6.
d. How much money did each person win?
Peter won $5250 and Sam won $1050.