Question

What is the cost of renting each item? (Hint: Solve the system of equations you selected in the previous problem, for x, y, and z.)


equation is 4Shoes + 5Harnesses +1Bags = 23
6Shoes + 6Harnesses + 0Bags = 30
3Shoes + 7Harnesses + 5Bags = 28

Answer 1

okay look at the 2nd equation that can be simplified

Answer 2

how so?

Answer 3

6Shoes + 6Harnesses + 0Bags = 30
6S + 6H = 30
divide both sides by 6

Answer 4

so 2?

Answer 5

SO IS IT TWO OR NOT?

Answer 6

no, not yet. he meant that
shoes + harnesses = 5

Answer 7

So we have:

4 shoes + 5 harnesses + 1 bag = 23
1 shoe + 1 harness = 5
3 shoes + 7 harnesses + 5 bags = 28


We can do substitution method:
1 shoe + 1 harness = 5
(1 shoe) = (5 - 1 harnesses) <-- got it?

Then using our first equation:
4 shoes + 5 harnesses + 1 bag = 23
4(5 - 1harnesses) + 1 bag = 23
20 - 4 harnesses + 1 bag = 23
-4 harnesses + 1 bag = 3 <-- We got a new equation with only 2 variables.

Now do you think you can do the same thing with the third equation, and get another 2 variable equation?

I assume that you know how to solve system of equations with only 2 equations and 2 variables right?

Answer 8

not entirely

Answer 9

This is an extension of this problem:

"Find x and y if:
ax + by = c
dx + ey = f"

I'm sure you learned that in class right? There's no way you would've have this problem if you haven't learned system of equations...

Answer 10

true that very true now that i look at it it makes sense

Answer 11

okay, soo um...back to our original question.

I'm gonna make shoes = s, harnesses = h, and b = bag:
First equation: 4s + 5h + 1b = 23
Second equation: 1s + 1h = 5
Third equation: 3s + 7h + 5b = 28

In the previous post, we used first and second equation to get:
-4h + 1b = 3

Now I want you to try to do the same thing with the second and third equation.
Yeah? Think you can do it? Cmon! :) (if you can't, just say so and I'll show you)

Answer 12

okay i tried but it makes zero sense

Answer 13

Okay so with the second and third equation: (I'll do the exact same thing)

We already got: -4h + 1b = 3

Now in order to be able to do system of equation for -4h + 1b = 3, we need another equation with 'h' and 'b' in it:

Second and Third Equations:
1s + 1h = 5
3s + 7h + 5b = 28

1s + 1h = 5
(1s) = (5 - 1h)

3(s) + 7h + 5b = 28
3(5 - 1h) + 7h + 5b = 28
15 - 3h + 7h + 5b = 28
4h + 5b = 13

So now we have:
4h + 5b = 13
-4h + b = 3

You can solve this thing right?

Answer 14

I vote with mhchen: Use the letters s, h, b to represent the rental cost of each the shoes, the harness and the bags.

Answer 15

What next? Know what to do? You have a system of 3 equations in 3 variables (s, h, b) and must solve for s, h and b.

Answer 16

i see. it still looks like too much i need it broken down individually

Answer 17

Make a choice: eliminate x first, or eliminate y first, or eliminate z first. Up to you!

Answer 18

x ill get that one