Question

a recipe that calls for $6\frac{3}{4}$ cups of marinade divides the marinade in two parts. the first part uses $2\frac{1}{2}$ cups of marinade. the second part uses the remaining cups.
lia makes 2.5 times the total number of cups of marinade for the recipe.
how much marinade, in cups, does lia make for the second part of the recipe?
a. $4\frac{1}{4}$
b. $16\frac{7}{8}$
c. $6\frac{1}{4}$
d. $10\frac{5}{8}$

Explanation:

Step1: Find original second part amount

Calculate the remaining marinade for the original recipe:
$$6\frac{3}{4} - 2\frac{1}{2} = \frac{27}{4} - \frac{5}{2} = \frac{27}{4} - \frac{10}{4} = \frac{17}{4} = 4\frac{1}{4}$$

Step2: Scale up by 2.5

Multiply the original second part by 2.5 (or $\frac{5}{2}$):
$$4\frac{1}{4} \times \frac{5}{2} = \frac{17}{4} \times \frac{5}{2} = \frac{85}{8} = 10\frac{5}{8}$$

Answer:

D. $10\frac{5}{8}$