Thread: An Algebra II Problem: Involving Gloves and Scarves I Have No Idea How to Do This

Hi,

You're buying scarves and gloves, as gifts for family members. Each scarf costs $3 less than each pair of gloves. Each pair of gloves costs $9. You buy 8 items for $66. How many scarves did you buy?

So, each scarf cost $6, Four scarves cost $24. Four pairs of gloves cost $36. That costs $60 total. I'm $6 short, but can only by 8 items.

Thanks-
Isabel

9g + 6s = 66
g + s = 8


(-9)g + (-9)s = (-9)8
-9g + -9s = -72

Subtract 9g + 6s = 66
-9g - 9s = -72
-3s = -6
s = 2
Scarves = 2 therefore Gloves = 6








6 Gloves and 2 Scarves

Originally Posted by stmsnyder1

Hi,

You're buying scarves and gloves, as gifts for family members. Each scarf costs $3 less than each pair of gloves. Each pair of gloves costs $9. You buy 8 items for $66. How many scarves did you buy?

So, each scarf cost $6, Four scarves cost $24. Four pairs of gloves cost $36. That costs $60 total. I'm $6 short, but can only by 8 items.

Thanks-
Isabel

the numbers here are small enough to figure out by trial and error. but in case you can't, here's a way to solve for the answer.

let s be the number of scarfs you buy. let g be the number of gloves you buy.

since you buy 8 items in all, s + g = 8

since each scarf costs $6 and each glove costs $9 and you spend $66 dollars in all, you have 6s + 9g = 66

thus you have two simultaneous equations with two unknowns, you can solve for s