mrs. lim buys 30 kg of cheese at a certain price.she finds that if she had bought some cheaper cheese costing 95 cents less she could have 32 1/2 kg for the same amount of moneyWhat is the price per kg of the more expensive cheese?
If the price is $p/kg,
30p = 32.5(p-.95)
p = 12.35
check:
30.00*12.35 = 370.50
32.50*11.40 = 370.50
To find the price per kilogram (kg) of the more expensive cheese, we can use the information provided in the problem.
Let's assume the price per kilogram of the more expensive cheese is "x" dollars.
According to the problem, Mrs. Lim buys 30 kg of the more expensive cheese. So, the total cost of the more expensive cheese would be 30x dollars.
Now, if Mrs. Lim had bought the cheaper cheese, she could have bought 32 1/2 kg for the same amount of money.
Let's calculate the cost of the cheaper cheese:
The cheaper cheese costs 95 cents less per kilogram than the more expensive cheese. So, the price per kilogram of the cheaper cheese would be (x - 0.95) dollars.
Therefore, the total cost of 32 1/2 kg of the cheaper cheese would be (32.5 * (x - 0.95)) dollars.
The problem states that the total cost of the more expensive and cheaper cheese is the same. So, we can equate the two total costs:
30x = 32.5 * (x - 0.95)
Now, let's solve this equation for "x" to find the price per kilogram of the more expensive cheese:
30x = 32.5x - 32.5 * 0.95
30x = 32.5x - 30.875
30x - 32.5x = - 30.875
-2.5x = -30.875
x = (-30.875)/(-2.5)
x ≈ 12.35
Therefore, the price per kilogram of the more expensive cheese is approximately $12.35.