Question

A grocery store sells two brands of sauerkraut. Brand X sells for ​$4.26 per jar while the​ No-Name brand sells for ​$3.62 per jar. If 33 jars were sold for a total of $133.54​, how many jars of each brand were​ sold?

There were ____ jar(s) of Brand X sold.

There were ____ jar(s) of No-name brand sold.

Answer 1

Solution:-

Let A be the No. of X brand items sold

Let B be the No. of no name brand items sold

X brrand sold for $4.26

NO name brand sold for $3.62

Total jars sold = A+B = 33 -------> EQUATION 1

Total amount of jars sold for = $133.54

A*4.26 + B*3.62 = $133.54 ---------> EQUATION 2

Multiply equation 1 with 3.62

A*3.62 + B*3.62 = $119.46 ----------> EQUATION 3

Substract equation 3 from equation 2

A*4.26 + B*3.62 - A*3.62 - B*3.62 = $133.54 - $119.46

A *0.64 = 14.08

A = 14.08 / 0.64

= 22

We can substitute A in From equation 1

22 + B = 33

B = 11

Therefore there are 22 jars of brand X were sold

There were  11 jars of No name brands were sold