Alvin spent half as much as lorie did on holiday presents this year and Chris spent 3 times more than alvin did. The total spent between the three of them was $720. How much did each person spend? show work!

The amount each person spend is as follows:

Lorie expenses = $240

Alvin expenses = 1 / 2 (240) = $120

Chris expenses = 3 / 2 (240)  = $360

let

Money Lorie spent = x

Therefore,

Alvin expenses = 1 / 2 x

Chris expenses = 3 (1 / 2 x) = 3 / 2 x

total amount spent = $720

Therefore,

3 / 2 x + 1 /2 x + x = 720

2x + x = 720

3x = 720

divide both sides by 3

3x / 3 = 720 / 3

x = 240

Lorie expenses = $240

Alvin expenses = 1 / 2 (240) = $120

Chris expenses = 3 / 2 (240)  = $360

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Alvin spent $120, Lorie spent $240 and Chris spent $360.

Step-by-step explanation:

Let,

Amount spent by Alvin = x

Amount spent by Lorie = y

Amount spent by Chris = z

Total amount spent by three of them = $720

According to given statement;

x =

2x=y

y = 2x     Eqn 1

z = 3x    Eqn 2

x+y+z=720    Eqn 3

Putting value of y and z from Eqn 1 and 2 in Eqn 3

Dividing both sides by 6

Putting x=120 in Eqn 1

y = 2(120) = 240

Putting x=120 in Eqn 2

z = 3(120) = 360

Therefore,

Alvin spent $120, Lorie spent $240 and Chris spent $360.

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step-by-step explanation: