Me and mom have been trying to solve this for hours. We need help. Can some one show us how to solve it. We do have a hint from the site we got the problem from. I will put it in the comments.
Ruth is knitting hats at a local fair. The booth cost 135 and the materials to make each hat cost 13. She plans on selling them for 18.
How many hats does she have to make to break even, and how much will sales and costs be at that point?
Let the number of hats be x
So the cost = 13x + 135 , which is the cost of the booth plus making the hats
income = 18x
so you want your income to be equal to the expenses
18x = 13x +135
5x = 135
x = 27
So making 27 hats would be the break-even point
check:
expenses = 27(13) + 135 = 486
income = 27(18) = 486
less than 27 hats would give you more expenses than income
more than 27 hats would give you a profit
so there you have it!
Your definition of "y = dollars" is rather meaningless. What dollars?
Hint: We need to come up with 2 linear equations based on the situation. Let x = hats and y = dollars. One of the equations will be y = 13x + 135. Determine the other equation, then solve for x and y using substitution.
By the way., we have 2 answer boxes for the question. One for the number of hats and another of the number of dollars. I also know how to do the substitution its just the other part that confuses me.
I don't know that's just the hint that was given.
To solve this problem, we need to find the number of hats Ruth has to make in order to break even and determine the amount of sales and costs at that point.
Let's break down the problem step by step:
Step 1: Calculate the profit per hat
The profit per hat is equal to the selling price minus the cost per hat. In this case, the selling price is $18, and the cost per hat is $13. So, the profit per hat is $18 - $13 = $5.
Step 2: Calculate the number of hats to break even
To break even, Ruth's total cost (including booth cost and material costs) should be equal to her total sales.
Let's assume she needs to make 'x' hats to break even.
The total cost is given by:
Total cost = Booth cost + (Cost per hat * Number of hats)
Total cost = $135 + ($13 * x)
The total sales is given by:
Total sales = Selling price per hat * Number of hats
Total sales = $18 * x
Since we want to find the number of hats to break even, we can equate the total cost to the total sales:
$135 + ($13 * x) = $18 * x
Step 3: Solve the equation for 'x'
To find the value of 'x', we can solve the equation.
$135 + ($13 * x) = $18 * x
Simplifying the equation:
$135 = $18 * x - $13 * x
$135 = $5 * x
Dividing both sides of the equation by $5:
$135/$5 = x
27 = x
Therefore, Ruth needs to make 27 hats to break even.
Step 4: Calculate the sales and costs at the break-even point
Now that we know the number of hats required to break even, we can calculate the sales and costs at that point.
Total cost at the break-even point:
Total cost = $135 + ($13 * 27) = $135 + $351 = $486
Total sales at the break-even point:
Total sales = $18 * 27 = $486
At the break-even point, Ruth needs to make 27 hats, and her sales will be $486, while her costs will also be $486.
Remember, this is just a step-by-step explanation of how to solve the problem. Feel free to ask if you have any questions or need further clarification.