Okay the questions is

I have 100 dollers to spend and I most buy 100 shoes.

Flip flops are .10 each
High heels are 2.00 each
boots are 5.00

You have to buy at least one of each.
I have been working hard on question and I feel like I am about to pull my hair out.

you need to by 10 pairs of flip flops and then you by 19 high heels and then 10 pairs of boots. You will have to figure out the rest.

sam

To solve this problem, we can start by figuring out the number of flip flops, high heels, and boots you need to buy.

Let's let F represent the number of flip flops, H represent the number of high heels, and B represent the number of boots.

Since you need to buy at least one of each, we have:

F ≥ 1
H ≥ 1
B ≥ 1

And the total number of shoes you need to buy is 100, so:

F + H + B = 100

Now, let's look at the cost of each type of shoe:

Flip flops cost $0.10 each, so the cost of flip flops would be:
0.10F

High heels cost $2.00 each, so the cost of high heels would be:
2.00H

Boots cost $5.00 each, so the cost of boots would be:
5.00B

The total cost of all the shoes should be $100, so:

0.10F + 2.00H + 5.00B = 100

Now, we have two equations:

F + H + B = 100
0.10F + 2.00H + 5.00B = 100

To solve this system of equations, we can use substitution or elimination. Let's use substitution to solve the equations.

From the first equation, we can express F in terms of H and B:

F = 100 - H - B

Now, substitute this expression for F in the second equation:

0.10(100 - H - B) + 2.00H + 5.00B = 100

Simplify the equation:

10 - 0.10H - 0.10B + 2.00H + 5.00B = 100

Combine like terms:

1.90H + 4.90B + 10 = 100

Subtract 10 from both sides:

1.90H + 4.90B = 90

Now we have one equation in terms of H and B. We can solve for H in terms of B by isolating H:

1.90H = 90 - 4.90B

Divide both sides by 1.90:

H = (90 - 4.90B) / 1.90

Now, we can substitute this expression for H back into the equation F = 100 - H - B:

F = 100 - [(90 - 4.90B) / 1.90] - B

Simplify the expression:

F = (100*1.90 - 90 + 4.90B - 1.90B) / 1.90

F = (190 - 90 + 3B) / 1.90

F = (100 + 3B) / 1.90

Now, we have expressions for F, H, and B in terms of only B. We can substitute these expressions into the equation F + H + B = 100:

(100 + 3B) / 1.90 + (90 - 4.90B) / 1.90 + B = 100

Combine like terms and multiply by 1.90 to clear the denominator:

100 + 3B + 90 - 4.90B + 1.90B = 1.90(100)

Simplify the equation:

100 + 90 + 3B - 4.90B + 1.90B = 190

Combine like terms:

-0.10B = 0

This equation tells us that B can be any value since any number multiplied by zero is zero. Therefore, there are infinitely many solutions for this problem.

However, if you want to find a specific solution, you can choose a value for B and solve for F and H using the expressions we derived earlier.

For example, let's say we choose B = 0. Plug this value into the expressions for F and H:

F = (100 + 3(0)) / 1.90 = 100 / 1.90 ≈ 52.63
H = (90 - 4.90(0)) / 1.90 = 90 / 1.90 ≈ 47.37

Since you cannot have a fraction of a shoe, we need to round F and H to the nearest whole number:

F ≈ 53
H ≈ 47
B = 0

So, if you choose not to buy any boots (B = 0), you would need to buy 53 flip flops and 47 high heels to have a total of 100 shoes.

Keep in mind that there are other possible combinations of F, H, and B that would satisfy the given conditions. Feel free to choose different values for B and solve for F and H to find other solutions.