Paint Town sold 45 paintbrushes, 1 kind at 48.50 each and another at $9.75 each. ?

Question

In all, $398.75 was taken in for the brushes. How many of each kind were sold?

Answer 1

i know you use algebra for that, but. i forgot.

Answer 2

ATTENTION: the correct sentence for the problem is:

Paint Town sold 45 paintbrushes, 1 kind at $8.50 each and another at $9.75 each.

So the price for the first type of paintbrushes is $8.50, not 48.50. That is asker's misspelling.

let's say they sold x paintbrushes at $8.50 each and y paintbrushes at $9.75 each

then you have:

x * 8,5 + y * 9.75 = 398.75

and

x + y = 45     | *(-8.5)

Multiply the second equation with -8.5. Then you have:

8,5x + 9.75y = 398.75

and

-8.5x - 8.5y = -382.5    ( -45 * 8.5 = -382.5)

Now add the 2 equations in only one, term by term (left terms and right terms):

8,5x + 9.75y - 8.5x - 8.5y = 398.75 - 382.5 =>

9.75y - 8.5y = 16.25 =>

1.25y = 16.25 =>

y = 16.25/1.25 =>

y = 13

Now, let's find the value of x. Consider the second equation from the system at the begining of this reply:

x + y = 45

replace y with 13:

x + 13 = 45 => x = 45 - 13 => x = 32

So the solution is:

x = 32 and y = 13, which means:

They sold

32 paintbrushes at $8.50 each

and

13 paintbrushes at $9.75 each

Answer 3

Hmmm..I think there's something wrong with the question but I don't know exactly what is it. If the paint town sold  45 paintbrushes at $9.75, that only kind of brush will cost $438.75. How about the paintbrush costing $48.50? And besides in $398.75 there will only be 8 $48.50 paintbrushes.

Answer 4

set up your equations first.  You need a system of 2 equations with 2 variables.

You have 2 types of brushes, x and y.  You sold 45 total, so x+y=45

You know x sold for 48.50 and y sold for 9.75 each and you made 398.75

So, 48.50x + 9.75y = 398.75

See if you can get it from there....

Answer 5

Let

X = number of Type 1 paintbrushes sold

Y = number of Type 2 paintbrushes sold

Equation 1 -- Paint Town sold 45 paintbrushes

X + Y = 45

Equation 2 -- 1 kind at 48.50 each and another at $9.75 each.



48.50X + 9.75Y = 398.75

<< How many of each kind were sold? >>

From Equation 1, Y = 45 - X and substituting this in Equation 2,

48.50X + 9.75(45 - X) = 398.75

48.50X + 438.75 - 9.75X = 398.75

38.75X = 398.75 - 438.75

38.75X = -40  --- from this, it is obvious that there is something wrong with the data given in the problem. The right hand side of the equation cannot be a negative number.

Answer 6

x+y=45

Because of the $ and 4 are together I assume that it is $ 8.50 and $9.75 is for the other and also that for common sense that one brush would be so much than another and there is no solution if it is a 4

x+y=45

8.5x+9.75y=398.75

x=45-y

8.5(45-y)+9.75y=398.75

382.50-8.5y+9.75y=398.75

1.25y= 16.25

y=13

x=32

32*8.5=272.00

13*9.75=126.75

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45 brushes @ 398.75