Question

Shawna and Kai both work at the same pet store. On Monday, Shawna counts 52 birds and cats in the store. For the same animals, Kai counts 138 legs. How many birds and cats are in the pet store?

There are____birds and____cats.

Answer 1

x= # of birds
y= # of cats

EQUATION 1:
x + y= 52

EQUATION 2:
birds= 2 legs
cats= 4 legs

2x + 4y= 138


STEP 1:
Solve for one variable in equation 1

x + y= 52
subtract y from both sides
x= 52 - y


STEP 2:
substitute x value in equation 2

2x + 4y= 138
2(52 - y) + 4y= 138
104 - 2y + 4y= 138
104 + 2y= 138
subtract 104 from both sides
2y= 34
divide both sides by 2
y= 17 cats


STEP 3:
substitute y value in either equation
x + y= 52
x + 17= 52
subtract 17 from both sides
x= 35 birds


CHECK:
2x + 4y= 138
2(35) + 4(17)= 138
70 + 68= 138
138= 138


ANSWER: There are 17 cats and 35 birds

Hope this helps! :)