# Stumped by a story problem: "A candy maker makes two sizes of candies...."

##### New member
Hello,
I can't figure out the order of operations to solve the following story problem. Could someone help me?

"[FONT=&quot]A candy maker makes two sizes of candies. Using the smaller size, a full jar will contain 120 pieces of candy. Using the larger candies a jar will contain 80 pieces of candy. The candy maker has a strict rule that no jars will contain a mix of small and large candies. If a store has room for 15 jars and they want 1560 total pieces of candy, how many jars will contain smaller candies?"[/FONT]

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello,
I can't figure out the order of operations to solve the following story problem. Could someone help me?

"A candy maker makes two sizes of candies. Using the smaller size, a full jar will contain 120 pieces of candy. Using the larger candies a jar will contain 80 pieces of candy. The candy maker has a strict rule that no jars will contain a mix of small and large candies. If a store has room for 15 jars and they want 1560 total pieces of candy, how many jars will contain smaller candies?"
Assume:

L = # of jars containing large candies

S = # of jars containing small candies

What equations and constraints can you write using these variables?

##### New member
Hope this helps....But I maybe wrong.

So, even though this question is asking for one answer. It is an equation in two variables. So, you have to find your 2 equations first. s=small candies jars and l=large candies jars
{120s + 80l=1560
{s + l=1560

Now you have to find a common denominator to remove one term. Let's eliminate "l" by multiplying to give it the coefficient -80.

(s+l)-80=15(-80)----> -80s-80l=-1200

Now Take your 2 Equations and Add.

120s + 80l=1560
+ -80s - 80l=-1200
40s = 360

Now divide each side by the coefficient of 40: 40s divided by 40 and 360 divided by 40.

s=9 jars, remember s is the small candies jars therefore;
to get the large jars would be:
15-9=6

Now to check the math:

Replace variable s with 9, and variable l with 6;
120(9)+80(6)=1560?
1080+480=1560?
1560=1560