Betty makes scarves and hats. Each scarf sells for $15 and each hat sells for $25. If she earned $180 from selling 8 items, how many of each kind of item were sold?

Question

What is the answer? (I'm bad at math😅)

Answer 1

Let S = #of scarves sold

Let H = number of hats sold.

We have two variables so we need two equations>

I. S + H = 8 (total number of items sold is 8)

Now let's consider money.

II. 15S + 25H = 180 ( Each scarf brings in $15, each hat brings in $25, and the total is $180).

To solve this system of two equations and two unknowns, one method is the substitution method (which is probably the way to go when it is easy to solve one of the equations for one of the variablss). Let's solve the first equation for S in terms of H.

S + H = 8

S = 8 - H.

Substitute the 8 - H for S in the 2nd equation.

15S + 25H = 180

15(8 - H) + 25H = 180

Solve that equation for H and you will have the number of hats sold. Hopefully an integer results, since you are not likely selling a fraction of a hat.

120 - 15H + 25H = 180

120 + 10H = 180

10H = 60

H = 6

Now solve for S;

S = 8 - H

S = 8 - 6 = 2

Check.

2 scarves @ $15 = $30

6 hats @ $25 = $150

And $150 + $30 = $180

Answer 2

To solve this problem you need to construct a system of liner equations. First, let's define some variables. We can can x the number of scarves sold and y the number of hats sold. Using these variables, and the fact that she sells scarves for $15 and hats for $25, we can say that the amount of money she makes for each would be 15x and 25y respectively. Therefore, we can express the total amount of money she makes from selling x scarves and y hats would be 15x + 25y. And since we know that she makes a total of $180, we can say that:

(1) 15x + 25y = 180.

Now, because we have two variables, we need two equations to solve this problem. The second equation comes from the fact that she sold a total of 8 items. Again, if she sells x scarves and y hats, that implies that:

(2) x + y = 8.

Now that we have our two equations we can solve this system using either substitution or elimination. Using substitution, we can rewrite equation (2) as:

y = 8 - x.

This lets us rewrite equation (1) as:

15x + 25(8 - x) = 180.

From here, you can solve for x, which tells you the number of scarves she sold. One you know what x is, you can plug that number back into equation (2) to get y, the number of hats she sold.