Question

Michael has x dollars saved. John has $18 more than Michael. Their friend Ian has $2 less than two-

thirds that Michael has. The total amount of money they have is $272. How much does Michael
have?

Answer 1

$96

Explanation:

Micheal's money = x

John's money = y

Ian's money = z

x + 18 = y

2/3x - 2 = z

x + y + z = $272

rearrange the equations we have:

2/3x = z + 2

x = 3/2(z + 2)

x = y - 18

Substitute y - 18 into x values:

3/2(z + 2) = y - 18

y - 18 + y + z = 272 --> 2y - 18 + z = 272

Solve for y:

Firstly rearrange

2y - 18 + z = 272 --> z = 272 + 18 - 2y, which simplifies to z = 290 - 2y

substitute into the formula:

3/2((290 - 2y) + 2) = y - 18

3/2(292 - 2y) = y - 18

438 - 3y = y - 18

4y = 456

y = $114

Substitute back into the formula to find z:

z = 290 - 2(114)

z = 290 - 228

z = $62

Put all of this back into one of the original formulas to find x:

x + y + z = 272

x + 114 + 62 = 272

x + 176 = 272

x = $96

Answer 2

Let,

• Michael has = x dollars
• John has = 18+x
• Ian has = 2-2/3x

Total amount = $272

Now, ATQ

`\tt \\rightarrow \: x + 18 + x + 2 - (2)/(3) x = 272`

`\tt \\rightarrow \: 2x + 20- (2)/(3) x = 272`

`\tt \\rightarrow \: 6x + 60 - 2x = 816`

`\tt \\rightarrow \: 4x + 60 = 816`

`\tt \\rightarrow \: 4x = 816 - 60`

`\tt \\rightarrow \: 4x = 756`

`\tt \\rightarrow \: x = 189`

➪ Thus, Michael has $189...~