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.
Answer:
37.5
Step-by-step explanation:
37.5 · 0.72 = 27
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.
Since a total of 47 hats where purchased, hence:
x + y + z = 47 (1)
Also, he spent a total of $302, hence:
5.5x + 6y + 7z = 302 (2)
He purchases three times as many medium hats as small hats, hence:
y = 3x
-x + 3y = 0 (3)
Represent equations 1, 2 and 3 in matrix form gives:
![\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C5.5%266%267%5C%5C-3%261%260%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D47%5C%5C302%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C5.5%266%267%5C%5C-3%261%260%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D47%5C%5C302%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C18%5C%5C23%5Cend%7Barray%7D%5Cright%5D)
Therefore he purchases 6 small hats, 18 medium hats and 23 large hats
250*0.62= 155
155 pounds is your answer.
