Question

Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he now and how many dogs did he walk?

Answer 1

Question is Incomplete;Complete question is given below;

Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he mow and how many dogs did he walk? $7.50 for walking dogs and $20 for mowing lawns

Answer:

Caleb mowed 3 lawns and walked 10 dogs.

Step-by-step explanation:

Let the number of dogs he walked be 'd'.

Let number of lawn he mowed be 'l'.

Given:

If he mowed half as many lawns as dogs walked

So we can say that;

$l=\frac{1}{2}d=0.5d \ \ \ \ equation\ 1$

Now given:

Cost for mowing each lawn = $20

Cost for walking each dog = $7.50

Total amount made = $105

Now we can say that;

Total amount made is equal to Cost for mowing each lawn multiplied by number of lawn he mowed and Cost walking each dog multiplied by number of lawn he mowed.

framing in equation form we get;

$20l+7.5d=105 \ \ \ \ \ equation \ 2$

Substituting equation 1 in equation 2 we get;

$20(0.5d)+7.5d=105$

Applying distributive property we get;

$10d+7.5d=105\\\\17.5d=105$

Dividing both side by 17.5 we get;

$\frac{17.5d}{17.5}=\frac{105}{17.5}\\\\d= 6$

Substituting the value of 'd' in equation 1 we get;

$l=0.5d=0.5\times6=3$

Hence Caleb mowed 3 lawns and walked 10 dogs.