Write as an equation: Mike, Carroll, and Jim empty their wallets and have $175 total. Mike has three times as much as Carroll. Carroll has twice as much money as Jim. How much money does each have?
A. [tex]j+2 j+3(2 j)=175[/tex]
B. [tex]3 j+2(3+j)=175[/tex]
C. [tex]j+2 j+3 j=175[/tex]
Answer (1)
Let j be the amount of money Jim has.
Carroll has 2 j and Mike has 3 ( 2 j ) = 6 j .
The equation representing the total money is j + 2 j + 6 j = 175 .
Solving for j , we find j = 9 175 , so Jim has 9 175 dollars, Carroll has 9 350 dollars, and Mike has 3 350 dollars.
Explanation
Understanding the Problem Let's break down this word problem step by step to turn it into an equation and then solve it!
Defining the Variable We're given that Mike, Carroll, and Jim have a total of $175 . We also know how their amounts of money relate to each other: Mike's amount is based on Carroll's, and Carroll's is based on Jim's. So, let's use Jim's amount as our starting point.
Expressing Each Person's Money in Terms of j Let j represent the amount of money Jim has. Since Carroll has twice as much money as Jim, Carroll has 2 j . And because Mike has three times as much money as Carroll, Mike has 3 ( 2 j ) = 6 j .
Formulating the Equation Now we can write an equation for the total amount of money: Jim's money ( j ) plus Carroll's money ( 2 j ) plus Mike's money ( 6 j ) equals $175 . This gives us the equation: j + 2 j + 6 j = 175
Simplifying the Equation Combining the terms on the left side, we get: 9 j = 175
Solving for Jim's Money To find out how much money Jim has, we divide both sides of the equation by 9: j = 9 175 ≈ 19.44 So, Jim has approximately $19.44 .
Calculating Carroll's Money Now we can find out how much Carroll and Mike have. Carroll has 2 j , so Carroll has: 2 j = 2 × 9 175 = 9 350 ≈ 38.89 Carroll has approximately $38.89 .
Calculating Mike's Money Mike has 6 j , so Mike has: 6 j = 6 × 9 175 = 9 1050 = 3 350 ≈ 116.67 Mike has approximately $116.67 .
Final Answer So, Jim has 9 175 dollars, Carroll has 9 350 dollars, and Mike has 3 350 dollars. The equation that represents the situation is: j + 2 j + 3 ( 2 j ) = 175
Stating the Solution The amount of money Jim has is 9 175 ≈ 19.44 dollars, Carroll has 9 350 ≈ 38.89 dollars, and Mike has 3 350 ≈ 116.67 dollars. The correct equation is j + 2 j + 3 ( 2 j ) = 175 .
Examples
Imagine you're planning a road trip with friends. You need to split the $175 gas money, but Sarah can only contribute half as much as you, and Mark can contribute three times as much as Sarah. By setting up an equation similar to the one we solved, you can figure out exactly how much each person needs to chip in to cover the gas costs fairly. This kind of proportional reasoning is useful in many real-life situations, from splitting bills to managing budgets!
