Question

A store sells two sizes of fresh wreaths. An​ 18-inch wreath costs ​$20​, and a​ 22-inch wreath costs ​$30. In one​ day, the number of​ 22-inch wreaths sold was four more than five times the number of​ 18-inch wreaths, for a total of ​$1310. How many of each were​ sold?

Answer 1

Let’s begin by setting
18-inch=X
22-inch=Y
We know that there was 4 more than 5 times the amount of 22 inch vs 18 inch so it can be shown like this

5x+4=y

We then can make a separate equation knowing that an 18-inch is $20 and a 22-inch is $30

20x+30y=1,310

So you now have 2 equations

5x+4=y
20x+30y=1,310

Let’s plug the first equation into the second equation, to solve for X

20x+30(5x+4)=1,310

20x+150x+120=1,310

170x=1,190

x=7

Now that we know X we can plug it back into the first equation

5(7)+4=y

39=y or y=39

You are now left with

x=7
y=39


You can check it by plugging your X and Y values into the 2nd equation

20(7)+30(39)=1,310

140+1,170=1,310

FINAL ANSWER

18-inch wreaths: 7

22-inch wreaths: 39