When Joey mowed lawns for 10 hours and walked dogo
for 4 hours, he made a total of $62. When he walked
dogs for 5 hours, and mowed the lawn for 8hours, he
made a total of $55. How much does Joey charge per hour
for each job? (Hint: let x. be charge per hour for mowing
lawns and y be the charge per hour for walking dogs).

Question

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absor201 absor201 · Answer 1 · 2019-12-19T13:37:26+01:00

The charges for mowing lawns are $5 per hour and charges for walking dogs are $3 per hour.

Step-by-step explanation:

Let,

x be the charge per hour for mowing lawns

y be the charge per hour for walking dogs

According to given statement;

10x+4y=62 Eqn 1

8x+5y=55 Eqn 2

Multiplying Eqn 1 by 5

[tex]5(10x+4y=62)\\50x+20y=310\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 4

[tex]4(8x+5y=55)\\32x+20y=220\ \ \ Eqn\ 4\\[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](50x+20y)-(32x+20y)=310-220\\50x+20y-32x-20y=90\\18x=90[/tex]

Dividing both sides by 18

[tex]\frac{18x}{18}=\frac{90}{18}\\x=5[/tex]

Putting in Eqn 1

[tex]10(5)+4y=62\\50+4y=62\\4y=62-50\\4y=12[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{12}{4}\\y=3[/tex]

The charges for mowing lawns are $5 per hour and charges for walking dogs are $3 per hour.

Keywords: linear equation, subtraction

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