Naomi Said:

Solving Linear System Equations Word Problems?

We Answered:

1. Let x = # of adult tix sold, y = # of student tix sold.
x + y = 550
20x + 12y = 9184
Solving by elimination
-8y = -1816
y = 227
x = 550 - 227 = 323
Check: 20(323) + 12(227) = 6460 + 2724 = 9184

2. y = 50x + 70
y = 54x + 42
Solving by substitution
50x + 70 = 54x + 42
4x = 28
x = 7
Check: 50(7) + 70 = 420 ; 54(7) + 42 = 420
For 7 hours choose either plumber.
For > 7 chose the 50/hr guy
For < 7 chose the 54/hr guy


3. 2w + l = 550
l = 3w + 75
Solving by substitution
2w + 3w + 75 = 550
5w = 475
w = 95
l = 360
Check: 3(95) + 75 = 360 ; 2(95) + 360 = 550
Dimensions are 95 x 360

I'll leave it to you to solve the next 2 (by substitution)

4. 0.04d + 0.05(15000 - d) = 690


5. y = 0.01x + 20000
y = 0.02x + 15000


6. This really doesn't make sense without indicating how long it took her to make the 500km trip.
You can easily say she drove the entire way at 100km/h taking 5 hours, or the entire way at 80km/h taking 6.25 hours,
or 5 hours at 80km/h and 1 hr a 100km/h ???