another problem i can't figure out?

Question

A company manufactures two products. One requires 2.5 hours of labor, 3 pounds of raw materials, and costs $42.40 each to produce. The second product requires 4 hours of labor, 4 pounds of raw materials, and costs $64.00 each to produce. Find the cost of labor per hour and the cost of raw materials per pound.

the answer is $11.20/hour labor; $4.80/pound materials

Answer 1

2.5L + 3M = 42.40
4L + 4M = 64.00 => L+ M = 16 => 2.5L + 2.5 m = 40

SUBTRACTING EQN 1 FROM EQN 2,
0.5M = 2.40
M = 4.80

L = 16 - M = 16 - 4.80 = 11.20

Answer 2

Let cost of labour be $x / hour
Let cost of raw materials be $y / hour
42.40 = 2.5 x + 3y
64.00 = 4x + 4y

-169.60 = -10x - 12y
192.00 = 12x + 12y-----ADD
22.40 = 2x
x = 11.20
64 = 44.80 + 4y
4y = 19.20
y = 4.80
Labour cost is $11.20 per hour
Material cost = $4.80 per hour

Answer 3

x = labor cost per hour
y = raw material cost per pound

1st equation (find value of x):
2.5x + 3y = $42.40
2.5x = $42.40 - 3y
x = ($42.40 - 3y) / 2.5
x = $16.96 - 1.2y

2nd equation (substitute value of x, find value of y):
4x + 4y = $64
4($16.96 - 1.2y) + 4y = $64
$67.84 - 4.8y + 4y = $64
$67.84 - $64 - 0.8y = 0
$3.84 = 0.8y
$3.84 / 0.8 = y
$4.80 = y
The cost of raw materials per pound is $4.80

1st equation (simplified, look for the $ value of x, substitute y):
x = $16.96 - 1.2($4.80)
x = $16.96 - $5.76
x = $11.20
The cost of labor per hour is $11.20

Proof (prove equality of the sides of each equation):

1st equation (substitute x and y):
2.5($11.20) + 3($4.80) = $42.40
$28.00 + $14.40= $42.40
$42.40 = $42.40

2nd equation (substitute x and y):
4($11.20) + 4($4.80) = $64.00
$44.80 + $19.20 = $64.00
$64.00 = $64.00

Answer 4

Let labour per hr is $x
and raw material per pound is $y
2.5x + 3y=42.4
10x+12y = 169.6...1st

4x+4y = 64
12x+12y = 192.......2nd
solving both we get
2x = 22.4
x=11.2
so y = 4.8
so labour per hr is $11.20
and raw material per pound is $4.8

Answer 5

2.5L + 3R = 42.40
4L + 4R = 64.00

4L + 4R = 64.00

4 R = 64-4L
R = 16-L
2.5L + 3(16-L) = 42.40
2.5L + 48 - 3L = 42.40
-0.5L = -5.60
0.5L = 5.60
L = 11.20
R = 16-11.20
R = 4.80