Sean, Tim, Fred and Mark paid a total of $132 for a souvenir. Mark paid 3/8 of what the rest paid. Sean paid 20% of what the rest paid. Tim and Fred paid an equal amount of money. How much did Fred pay?
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First , rest paid = $132
Now , Mark paid 3/8 of what the rest paid. i.e.
rest paid = 132(1 - 3/8) = $82.5
and Sean paid 1/5 of what the rest paid. i.e.
rest paid = 82.5(1 - 1/5) = $66
Since , Tim and Fred paid an equal amount of money. i.e.
Fred paid = 66/2 = 33
Thus , Fred paid $33 amount of money.
To find out how much Fred paid, let's break down the information we have step by step.
1. We know that Mark paid 3/8 of what the rest paid.
Let's say the amount Mark paid is "M".
2. We also know that Sean paid 20% of what the rest paid.
Let's say the amount Sean paid is "S".
3. Tim and Fred paid an equal amount of money.
Let's say the amount Tim and Fred paid is "T".
Now, let's translate the given information into equations to solve for the unknowns.
1. We know that Mark paid 3/8 of what the rest paid.
So, Mark's payment (M) can be expressed as:
M = (3/8)(S + T)
2. We also know that Sean paid 20% of what the rest paid.
So, Sean's payment (S) can be expressed as:
S = 0.2(S + T)
3. Tim and Fred paid an equal amount of money.
So, Tim's payment (T) and Fred's payment (F) can be expressed as:
T = F
Now, let's combine these equations to solve for Fred's payment (F).
Given that Mark, Sean, Tim, and Fred paid a total of $132, we can write the equation as:
M + S + T + F = 132
Substituting the derived equations for M, S, and T, we have:
(3/8)(S + T) + 0.2(S + T) + T + F = 132
Let's simplify this equation:
(3/8)(S + T) + (1/5)(S + T) + T + F = 132
Combining the fractions:
(15/40)(S + T) + (8/40)(S + T) + T + F = 132
Simplifying the equation further:
(23/40)(S + T) + T + F = 132
Now, since T = F, we can substitute T for F:
(23/40)(S + F) + T + F = 132
Simplifying the equation:
(23/40)(S + F) + 2T = 132
Now let's calculate the values of S + F and 2T:
Since T = F, we can write S + 2T = 132
This implies S + F = 132/3 = 44
Now, let's substitute S + F = 44 into the equation:
(23/40)(44) + 2T = 132
Simplifying the equation:
(23/40)(44) + 2T = 132
Multiply both sides of the equation by 40 to remove the fraction:
23(44) + 80T = 132 * 40
Simplifying further:
1012 + 80T = 5280
Subtract 1012 from both sides of the equation:
80T = 5280 - 1012
80T = 4268
Divide both sides by 80 to solve for T:
T = 4268 / 80
T = 53.35
Since Tim and Fred paid an equal amount, we can round T to the nearest whole number:
T ≈ 53
Therefore, Fred paid approximately $53.