Math  /  Algebra

Question3. Given the supply function, P=500+2QP=500+2 Q, where PP is the price of a bottle of a perfume, QQ is the number of litres supplied. a) What is the value of QQ when P=K750P=K 750 ? b) What is the value of P when Q=35Q=35 ?

Studdy Solution

STEP 1

1. The supply function is given as P=500+2Q P = 500 + 2Q , where P P is the price and Q Q is the quantity supplied.
2. We are to find the value of Q Q when P=750 P = 750 .
3. We are to find the value of P P when Q=35 Q = 35 .
4. The relationship between P P and Q Q is linear.

STEP 2

1. Solve for Q Q when P=750 P = 750 .
2. Solve for P P when Q=35 Q = 35 .

STEP 3

Start with the supply function P=500+2Q P = 500 + 2Q and set P=750 P = 750 .
750=500+2Q 750 = 500 + 2Q

STEP 4

Isolate 2Q 2Q by subtracting 500 from both sides.
750500=2Q 750 - 500 = 2Q
250=2Q 250 = 2Q

STEP 5

Solve for Q Q by dividing both sides by 2.
Q=2502 Q = \frac{250}{2}
Q=125 Q = 125

STEP 6

Start with the supply function P=500+2Q P = 500 + 2Q and set Q=35 Q = 35 .
P=500+2(35) P = 500 + 2(35)

STEP 7

Simplify the expression by calculating 2×35 2 \times 35 .
P=500+70 P = 500 + 70

STEP 8

Add 500 and 70 to find P P .
P=570 P = 570
Solution: a) When P=750 P = 750 , the value of Q Q is 125 125 . b) When Q=35 Q = 35 , the value of P P is 570 570 .

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