algebra 2 problem! help?

Question

gwen sold magazine subscriptions with three different prices : $16, $14 , $24 .she sold total 29 subscriptions.
her total amount sale was $548 . how many $24 sunsciptions did gwen sale ?
thank u

Answer 1

s # of $16 sub
f # of $14 sub
t # 0f $24 sub

1) s+f+t=29
2) 16s + 14f + 24t = 548

16X 1) 16s + 16f + 16t = 464 subtract 2)
-16s - 14f - 24t = -548

3) 2f -8t = -84 since we can't have a fraction of a subscrip
Let's look for a whole number solution

f ..... t
0 ... 8 1/2
1 ... 8 3/4
2 ... 11 ...... 11 subscriptions of $24, 2 of $14 , 16 of $16
I can see that f must 4mod2
6 ..... 12 ......... 12 subscriptions of $24, 6 of $14 , 11 of $16
10 ... 13 ......... 13 subscriptions of $24, 10 of $14 , 6 of $16
14 ... 14 ......... 14 subscriptions of $24, 14 of $14 , 1 of $16

You have a few choices.

Answer 2

I kinda doubt this is what your algebra 2 teacher had in mind, but there are only four integral solutions. The number of $24 subscriptions can be 11, 12, 13, or 14. Each gives a unique solution for the number of $14 and $16 subscriptions.

As another poster said, you must be leaving out part of the problem.

Answer 3

if she had sold 29 subscriptions with only prices $16 and $14then the total money would be 20*29 = 580
the difference : 580 - 548 = 32
24 - 20 = 4
the number of subscriptions sold : 32/4 = 8

Answer 4

This is a 3 variable problem with only two equatons
x+y+z=29

16x+14y+24z= 548

Not enough info to solve.