Can anyone me on this problem? it doesn’t make sense to

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.

The student council made more snow cones per hour than the parent volunteers.

Explanation:

To find the number of snow cones made per hour:

XXX

Divide the number of snow cones made

XXX

by the number of hours spent making snow cones.

Parent volunteers

XXX

Number of snow cones:  

120

XXX

Number of hours spent making snow cones:  

5

Number of snow cones per hour:  

120

÷

5

=

24

Student council

XXX

Number of snow cones:  

100

XXX

Number of hours spent making snow cones:  

4

Number of snow cones per hour:  

100

÷

4

=

25

Since the student council made  

25

snow cones per hour and the parent volunteers only made  

24

snow cones per hour:

the student council made more snow cones per hour.

Step-by-step explanation: