A baker needs between 40 pounds 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?
The question as it is does not restrict the answer to integral weights in pounds, so any between 40 and 50 pounds is a possible weight, W.
In order to satisfy the given proportion constraints, W/11=sugar, 10W/11=flour will ensure that the proportion be correct.
If the question specifies that the ingredient weights be integral (i.e. whole numbers), then W will have to be a multiple of 11, which makes 44 the only possible weight of mixture between 40 and 50, and the weight of flour is 10W/11=40 pounds.
Let's solve this step-by-step:
Step 1: Let's assume the weight of sugar in the mixture is "x" pounds.
Step 2: Since the mixture contains ten times as much flour as sugar, the weight of flour in the mixture would be 10x pounds.
Step 3: The total weight of the mixture is the sum of the weight of flour and sugar, which is x + 10x = 11x pounds.
Step 4: According to the problem statement, the baker needs between 40 pounds and 50 pounds of the mixture. Therefore, we can set up the inequality: 40 ≤ 11x ≤ 50.
Step 5: Divide all sides of the inequality by 11 to solve for x: 40/11 ≤ x ≤ 50/11.
Step 6: Simplify the fractions: approximately 3.64 ≤ x ≤ 4.55.
Step 7: Since we can't have a fractional weight for sugar, we can round the values up to the nearest whole number.
Step 8: Therefore, the possible weights of sugar that the baker can use are 4 pounds and 5 pounds.
Step 9: Finally, to find the weight of flour, we can multiply the weight of sugar by 10: 4 pounds * 10 = 40 pounds and 5 pounds * 10 = 50 pounds.
Step 10: So, the possible weights of flour the baker can use are between 40 pounds and 50 pounds.
To find the possible weights of flour the baker can use, we need to determine the range of weights for flour in the flour-sugar mixture.
Let's assume the weight of sugar in the mixture is "x". According to the given information, the weight of flour in the mixture is ten times the weight of sugar, so it would be "10x".
Now, the total weight of the mixture is the sum of the weights of flour and sugar. Since the baker needs between 40 pounds and 50 pounds of the mixture, we can set up the following inequality:
40 ≤ 10x + x ≤ 50
Simplifying the inequality, we get:
40 ≤ 11x ≤ 50
Divide all sides of the inequality by 11 to solve for "x":
40/11 ≤ x ≤ 50/11
Therefore, the weight of sugar "x" in the mixture must be between approximately 3.64 pounds (40/11) and 4.54 pounds (50/11).
Since the weight of flour is ten times the weight of sugar, the weight of flour would be:
10 * 3.64 ≤ weight of flour ≤ 10 * 4.54
Therefore, the possible weights of flour the baker can use range from approximately 36.4 pounds (10 * 3.64) to 45.4 pounds (10 * 4.54).