Question

Martin had M dollars initially. First, Martin spent 1/3 of his money. Then Martin spent 3/4 of what was left. Finally, Martin spent another $20. Write an expression in terms of M for the final amount of money that Martin has. Then write another equivalent expression. Explain.

Answer 1

Martin initially spent 1/3 of his money, then 3/4 of the remainder, and finally another $20. The final amount of money he has can be expressed as ((2/3)M × (1/4)) - $20 or equivalently as (1/6)M - $20.

Step-by-step explanation:

The student wants to know the final amount of money that Martin has after several transactions, expressed in terms of his initial amount M. Initially, Martin spent 1/3 of his money, so he was left with 2/3 of M. Then, Martin spent 3/4 of what remained, leaving him with 1/4 of the 2/3 of M. Finally, Martin spent an additional $20.

First expression: The final amount of money Martin has can be expressed as: ((2/3)M × (1/4)) - $20.

Second expression: Simplifying the first expression, we get an equivalent expression: (1/6)M - $20.

Answer 2

First Method

First, he had M some unknown amount

Then, he had 2/3 M since he spent 1/3 M

Then, he spent 3/4 of the (2/3 M) so he had 1/4 of the ( 2/3M)

Then, he spent what was left $20 so $20 = 1/4 ( 2/3 M) now solve for M

You can check by doing each step and figuring how much was spent and how much was left.

Second Method

let us consider the left amount be Y and total now of M dollar be X

Y = amount of money Nartin has left

Y = X - ( 1/3 ) ( X ) - ( 3/4 ) ( X - 1/3 X ) - 20

Y = X - 1/3 X - 3/4 X + 3/12 X - 20

Y = X - 4/12 X - 9/12 X + 3/12 X - 20

Y = X - 10/12 X - 20

Y = X - 5/6 X - 20

Y = ( 1 / 6 ) ( X ) - 20

Hope this helps.