help with math (problem solving question)?

Question

an electronics firm makes two types of switching devices. type A takes 4 minutes to makes and requires $3 worth of materials. type B takes 5 minutes to make and requires $5 worth of materials. when the production manager reviewed the latest batch, he found that it took 35 hours to make these switches with a materials cost of $900. how many switches of each type were produced for this latest batch?

Answer 1

___________Type A_____Type B___Total
Time(min)_____4_________5_______2100
Cost ($)______3_________5________900
No. made_____x_________y

4x + 5y = 2100
3x + 5y = 900

x = 1200

3600 + 5y = 900
5y = 900 - 3600
5y = - 2700
y = - 540

Would appear to be an error in question due to - ve value for y.

Answer 2

First, get 35 hours in minutes, or 2100.

Next, set up two equations, where "A" is the qty of type A parts, and B is the quantity of type "B" part.

2100 = 4A + 5B <===time to make parts
900 = 3A + 5B <==== Cost of parts

Next, multiply both sides of the second equation by -1 and add the two equations together (to get the B terms to drop out).

2100 = 4A + 5B
-900 = -3A - 5B
-----------------------
1200 = A

Substitute 1200 for A into either equation above, and B must be -540.

You must have a problem with your numbers, because you can't make -540 of a product (I triple checked).

Answer 3

Let A = number of switch A
Let B = number of switch B

Total time to make A + B switches is:
4A + 5B = 35*60 or
4A + 5B = 2100

Total cost to make A + B switches is:
3A + 5B = 900

Combining the two equations into a system for solving,
4A + 5B = 2100
3A + 5B = 900
--------------------------------------------- Subtracting the two eqs.
A = 1200 switches

Substitue 1200 for A to get

3(1200) + 5B = 900
3600 - 900 = -5B uh oh...
2700 = -5B
B = -540 switches, which is impossible. Pls check your problem.

Answer 4

for type a:
t=4, c=3

for type b:
t=5, c=5

35 hours = 35x60mins = 2100mins

cost = 900 = 3a +5b
time = 2100 = 4a +5b

ok, now see if you can solve it. (hint - DONT just solve these as simultaneous equations...)

Answer 5

Hey I'm here for the first time. I came across this question and I find the replies really useful. I'm hoping to give something back and assist others too.

Answer 6

35....