Question

flour in recipes
0 1/2 1 1 1/2 2 2 1/2 3 3 1/2 4
flour (cups)
how many cups of flour is needed to complete all 10 recipes?
a. 10 1/2 cups
b. 15 1/2 cups
c. 2 1/2 cups
d. 14 1/2 cups

Explanation:

Step1: Count X at each flour amount

• At $\frac{1}{2}$: 3 X's, so total flour: $3\times\frac{1}{2}=\frac{3}{2}$
• At $1$: 2 X's, so total flour: $2\times1 = 2$
• At $1\frac{1}{2}$: 1 X, so total flour: $1\times1\frac{1}{2}=\frac{3}{2}$
• At $2$: 2 X's, so total flour: $2\times2 = 4$
• At $2\frac{1}{2}$: 1 X, so total flour: $1\times2\frac{1}{2}=\frac{5}{2}$
• At $3$: 1 X, so total flour: $1\times3 = 3$

Step2: Sum all the amounts

Convert all to halves for easier addition:

• $\frac{3}{2} + 2+\frac{3}{2}+4+\frac{5}{2}+3$
• $2=\frac{4}{2}$, $4=\frac{8}{2}$, $3=\frac{6}{2}$
• Sum: $\frac{3 + 4+ 3+ 8+ 5+ 6}{2}=\frac{29}{2}=14\frac{1}{2}$? Wait, no, wait, let's recount the X's. Wait the problem says 10 recipes. Let's check the X count again.

Wait the line plot: let's count the X's:

• At $\frac{1}{2}$: 3 X (so 3 recipes)
• At $1$: 2 X (2 recipes)
• At $1\frac{1}{2}$: 1 X (1 recipe)
• At $2$: 2 X (2 recipes)
• At $2\frac{1}{2}$: 1 X (1 recipe)
• At $3$: 1 X (1 recipe)

Total recipes: 3+2+1+2+1+1=10, correct.

Now calculate total flour:

• $3\times\frac{1}{2} = \frac{3}{2}$
• $2\times1 = 2$
• $1\times1\frac{1}{2} = \frac{3}{2}$
• $2\times2 = 4$
• $1\times2\frac{1}{2} = \frac{5}{2}$
• $1\times3 = 3$

Now sum:

$\frac{3}{2} + 2 + \frac{3}{2} + 4 + \frac{5}{2} + 3$

Convert to fractions with denominator 2:

$\frac{3}{2} + \frac{4}{2} + \frac{3}{2} + \frac{8}{2} + \frac{5}{2} + \frac{6}{2}$

Add numerators: 3+4+3+8+5+6=29? Wait 3+4=7, +3=10, +8=18, +5=23, +6=29. So $\frac{29}{2}=14\frac{1}{2}$? Wait but let's check again. Wait maybe I miscounted the X's. Wait the plot:

Looking at the plot:

• $\frac{1}{2}$: 3 X (so 3)
• $1$: 2 X (so 2)
• $1\frac{1}{2}$: 1 X (1)
• $2$: 2 X (2)
• $2\frac{1}{2}$: 1 X (1)
• $3$: 1 X (1)

3+2+1+2+1+1=10. Correct.

Now calculate each part:

3*(1/2) = 3/2

2*1 = 2 = 4/2

1*(3/2) = 3/2

2*2 = 4 = 8/2

1*(5/2) = 5/2

1*3 = 3 = 6/2

Now sum numerators: 3 + 4 + 3 + 8 + 5 + 6 = 29. 29/2 = 14.5 = 14 1/2. So the total is 14 1/2 cups.

Answer:

D. $14\frac{1}{2}$ cups