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Alex, Ben, and Carl have some money. If Alex gives $4.55 to Ben, the two boys will have an equal amount of money. If Ben gives $4.55 to Alex, Alex will have 3 times as much money as Ben. Carls amount of money is the sum of the two other boys' money. How much do the three boys have in all?

User Ben Pap
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$72.80 Let's create a series of equations to express what we know. I'll use the variables A,B,C to represent respectively Alex's, Ben's and Carl's money. "If Alex gives $4.55 to Ben, the two boys will have an equal amount of money." A - 4.55 = B + 4.55 "If Ben gives $4.55 to Alex, Alex will have 3 times as much money as Ben. A + 4.55 = (B - 4.55)*3 Carls amount of money is the sum of the two other boys' money. How much do the three boys have in all? C = A + B Let's take the 1st equation and solve for A A - 4.55 = B + 4.55 A = B + 4.55 + 4.55 A = B + 9.10 Now let's take the 2nd equation and substitute (B+9.10) for A and then solve for B. A + 4.55 = (B - 4.55)*3 (B+9.10) + 4.55 = (B - 4.55)*3 B + 9.10 + 4.55 = 3B - 3*4.55 B + 13.65 = 3B - 13.65 13.65 = 2B - 13.65 13.65 + 13.65 = 2B 2*13.65 = 2B 13.65 = B So Ben has 13.65. Let's use that to calculate Alex's money. A = B + 9.10 A = 13.65 + 9.10 A = 22.75 And now we know that Alex has 22.75, let's use that and Ben's amount to calculate Carl's C = A + B C = 22.75 + 13.65 C = 36.40 So Alex has $22.75, Ben has $13.65, and Carl has $36.40. Since we're looking for the total amount of money the boys have, that is: $22.75 + $13.65 + $36.40 = $72.80
User SecStone
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