1x is two times greater than 1y and equals 280

Question

Joe sold popcorn and water at the basketball game. Each popcorn cost $1.00 and each water cost $2.00. Joe collected a total of $280. If the number of popcorn sold was three times the number of waters sold, how many of each was sold?

Answer 1

Hi Dalton,

 

Do you have a strategy for approaching word problems? If not, you can try the one laid out in this answer. I always suggest you start by writing out the important information and defining the variables you are going to use to solve this problem. We can write it like this:

• p=popcorn
• w=water
• $1.00 per popcorn
• $2.00 per water
• Total earned is $280

Now, we need to write the two equations needed to solve. We have to translate the 3 sentences which will give us the 2 equations needed. The phrase "the number of popcorn sold was three times the number of waters sold" can be written algebraically as p=3w.

 

The second equation is a little harder to see right away. The sentences "each popcorn cost $1.00 and each water cost $2.00. Joe collected a total of $280" can be algebraically translated as $1.00p+$2.00w=$280. We want to end up with just dollars and know that we have to multiply the cost by the variable because the units are (dollars/number) times number, leaving us with just dollars when we simplify.

 

After you have your two equations written, you can see that this is a substitution problem. By substituting 3w for p in the second equation, you can now find how many waters were sold. The second equation now looks like this: $1.00(3w)+$2.00w=$280. Once you solve for w, you can now substitute that numeric value back into either the first or original second equation to solve for p, but it's easier to choose the simpler equation. In this case, it's the first one.

Answer 2

Joe sold popcorn and water at the basketball game. Each popcorn cost $1.00 and each water cost $2.00. Joe collected a total of $280. If the number of popcorn sold was three times the number of waters sold, how many of each was sold?

 

let x be the number of popcorns sold

let y be the number of water sold

 

From the problem statement $1.x + $2.y=$280.00, x+2y=280 ...Eq1

also the number of popcorn sold is three times the number of water, then x = 3y ...Eq2. Substitute the value of x in Eq 1

 

3y+2y=280, 5y=280, y= 56, x=3(56)=168 ... check

 

168+2(56)=280...checks No of popcorn sold = 168

                                     No of waters sold = 56