Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
By the Pythagorean Theorem:
The square of the hypotenuse (longest side) of a right triangle is equal to the sum of the side lengths squared, or mathematically:
h^2=x^2+y^2, where x and y are the side lengths and h is the length of the hypotenuse, in this case:
9.4^2=6.8^2+GF^2
GF^2=9.4^2-6.8^2
GF^2=42.12
GF=√42.12 units
GF≈6.49 units (to nearest hundredth of a unit)
Answer:
the answer will be 18 ohkay but they will eill have more dimes than quarters
I honestly have no idea. Geometry is my worst subject
