Word Problem

Question

party supplies inc. sells metallic balloons for $2 each and helium balloons for $3.50 per bunch. Yesterday, hey sold 36 more metallic balloons than the number of bunches of helium balloons. The total sales for both type of balloons were $281. How many metallic balloons were sold and how many bunches of helium balloons are sold?

Answer 1

Let m be the number of metallic balloons and h be the number of bunches of helium balloons.

 

The number of metallic balloons sold (m) was 36 more than the number of bunches of helium balloons (h).

 

So:

 

m = h + 36

 

Also, the total price of the balloons is equal to the sum of $2 times the number of metallic balloons (m) and $3.50 times the number of bunches of helium balloons (h).

 

We can write this as:

 

2m + 3.5h = 281

 

Now, using substitution (substitute m in the first equation for m in the second), we get:

 

2(h + 36) + 3.5h = 281

 

2h + 72 + 3.5h = 281

 

5.5h + 72 = 281

 

5.5h = 281 - 72

 

5.5h = 189

 

5.5h/5/5 = 189/5.5

 

h = 38 (bunches of helium balloons)

 

m = h + 36 = 38 + 36 = 74 (metallic balloons)