Im trying to find h

[nkb]

h = hours worked in day
t = set-up time
s = speed
c = unit cost
p = unit price

Profit generated = Units produced × Profit per unit
= (h-t) × s × (p-c)

Profit for A = (h-4) × 3 × (5-3.5)
= 4.5(h-4)

Profit for B = (h-5) × 1 × (12-5)
= 7(h-5)

There is a day length at which profit is equal for either product, when:
4.5(h-4) = 7(h-5)

I don't know how to go further with this equation in order to find h. I know that the answer is:

2.5h = 17
h = 6.8

but I don't understand how to get from

4.5(h-4) = 7(h-5) to
2.5h = 17

 

[tkhunny]

Distributive Property of Multiplication over Addition.

a(b+c) = ab + ac

Do that.

 

[nkb]

I don't understand

 

[tkhunny]

You have: "4.5(h-4) = 7(h-5)"

Apply the principle on each side.

 

[nkb]

I don't understand

 

[nkb]

so:
4.5h -18 = 7h - 35

subtract 4.5h from both sides;

-18 = 2.5h - 35

then add 35 to both sides;

17 = 2.5h

therefore h = 17 / 2.5 = 6.8?

 

[mmm4444bot]

… therefore h = 17 / 2.5 = 6.8?

You can check, by substitution, in the original equation.

4.5(h - 4) = 7(h - 5)

4.5(6.8 - 4) = 7(6.8 - 5)

Simplify each side. If you get a true statement, then 6.8 is the solution. :cool:

 

[tkhunny]

I don't understand

You'll have to do better than that. You should have studied various properties, associative, commutative, inverse, distributive, reflexive. Have you seen these things? You will need them. Better back up and review before continuing to struggle in this way.