A baker needs between 40 and 50 pounds of a flour-sugar mixture that contains ten times as much flour as sugar. What are the possible weights of flour the baker can use?

Would I set it up like:
40+10x<x<50+10x

40<F+S<50

where F+S=F+F/10=1.1F
40<1.1F<50

that makes no sense at all because (1) you have ten TIMES as much flour so why would you divide and (2) 1.1 is not anywhere close to being in between 40 and 50

If you let F = the amount of flour, and let S = the amount of sugar, then bobpursley is correct in that 40 < 1.1F < 50

Divide by 1.1 to find a range for the amount of flour.

In response to your queries:
(1) Multiplying or dividing depends entirely on the way you set up the equation.

(2) Divide 40 and 50 by 1.1, 1.1 is not the answer.

To solve this problem, you need to set up an equation based on the given information and use algebra to find the range of possible weights for the flour.

Let's assume the weight of sugar in the mixture is represented by the variable "x". Since the mixture contains ten times as much flour as sugar, the weight of flour would be 10x.

According to the problem, the baker needs between 40 and 50 pounds of the flour-sugar mixture.

So, we can set up the following inequality:
40 ≤ 10x + x ≤ 50

To simplify the equation, combine the x terms:
40 ≤ 11x ≤ 50

Now, divide each part of the inequality by 11 to solve for x:
40/11 ≤ x ≤ 50/11

This gives us the range of possible weights for sugar: 3.64 ≤ x ≤ 4.55

Finally, since we know the weight of flour is 10 times the weight of sugar, we can multiply the range of sugar weights by 10 to find the corresponding range of flour weights:

10(3.64) ≤ 10x ≤ 10(4.55)
36.4 ≤ 10x ≤ 45.5

Therefore, the possible weights of flour the baker can use are between 36.4 and 45.5 pounds.