the number of calculators mrs. hopkins can buy for the classroom varies inversely as the cost of each calculator. she can buy 24 calculators that cost $60 each. how many calculators can she buy if they cost $80 each?
Let x = number of calculators she can buy,
80x=60*24
x=60*24/80 = 18
Mrs Hopkins can buy 18 calculators at $80 each.
To solve this problem, we need to use the concept of inverse variation. Inverse variation means that as one quantity increases, the other decreases, and vice versa. In this case, the number of calculators is inversely proportional to the cost of each calculator.
We can set up a proportion to solve for the unknown quantity. Let's denote the number of calculators as 'n' and the cost of each calculator as 'c'. According to the given information:
n ∝ 1/c
To solve for the constant of variation, we can use the initial values given. When 24 calculators are bought at $60 each, we have:
24 ∝ 1/60
Next, we can use this proportion to find the number of calculators that can be bought if the cost is $80 each. Let's denote this quantity as 'x'.
x ∝ 1/80
Now, we can set up the proportion using the two values we have:
24/60 = x/80
To solve for 'x', we can cross-multiply and solve the equation:
24 * 80 = 60 * x
1920 = 60x
Dividing both sides by 60, we find:
x = 32
Therefore, Mrs. Hopkins can buy 32 calculators if they cost $80 each.