Suppose that we strike a bargain, and we agree that in this chapter, for every problem you do right, I will pay you $.86 and that for every problem you do wron, I will fine you $.47. After 28 problems, you have a nice sum of $9.45 in your pocket (and I am looking for a way out of the deal). How many problems did you do correctly?
.86C-.47W=9.45
C+W=28
for math we are doing proportions and cuostomary mesurments 5 cups is less than or greater than 40 fluid ounces
To solve the problem, we need to use the given equations and solve for the number of problems done correctly (C).
Let's start by using the second equation, which states that C + W = 28. Rearranging this equation, we get W = 28 - C.
Substituting this value of W into the first equation, we have:
0.86C - 0.47(28 - C) = 9.45
Next, let's simplify the equation:
0.86C - 0.47(28 - C) = 9.45
0.86C - 13.16 + 0.47C = 9.45
1.33C - 13.16 = 9.45
Now, let's isolate C by adding 13.16 to both sides:
1.33C - 13.16 + 13.16 = 9.45 + 13.16
1.33C = 22.61
To find the value of C, divide both sides of the equation by 1.33:
C = 22.61 / 1.33
C ≈ 17
Therefore, the number of problems done correctly (C) is approximately 17.