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Moses has a bakery, and he is expecting a new shipment of flour today.
The number of loaves, 
N, that Moses will bake today given that he receives 
k kilograms of flour is given by the function

N(k)=10+3k". "
The income, 
I, in dollars, that Moses makes from baking 
x loaves of bread is given by 
I(x)=6x.
Which expression models Moses's income for the day if he receives 
k kilograms of flour?
Choose 1 answer:
(A) 
60+3k
(B) 
10+9k
(C) 
60+18 k
(D) 
10+18 k

Moses has a bakery, and he is expecting a new shipment of flour today.\newlineThe number of loaves, N N , that Moses will bake today given that he receives k k kilograms of flour is given by the function\newlineN(k)=10+3k N(k)=10+3 k \text {. } \newlineThe income, I I , in dollars, that Moses makes from baking x x loaves of bread is given by I(x)=6x I(x)=6 x .\newlineWhich expression models Moses's income for the day if he receives k k kilograms of flour?\newlineChoose 11 answer:\newline(A) 60+3k 60+3 k \newline(B) 10+9k 10+9 k \newline(C) 60+18k 60+18 k \newline(D) 10+18k 10+18 k

Full solution

Q. Moses has a bakery, and he is expecting a new shipment of flour today.\newlineThe number of loaves, N N , that Moses will bake today given that he receives k k kilograms of flour is given by the function\newlineN(k)=10+3k N(k)=10+3 k \text {. } \newlineThe income, I I , in dollars, that Moses makes from baking x x loaves of bread is given by I(x)=6x I(x)=6 x .\newlineWhich expression models Moses's income for the day if he receives k k kilograms of flour?\newlineChoose 11 answer:\newline(A) 60+3k 60+3 k \newline(B) 10+9k 10+9 k \newline(C) 60+18k 60+18 k \newline(D) 10+18k 10+18 k
  1. Understanding the relationship: Understand the relationship between the number of loaves and kilograms of flour. The function N(k)=10+3kN(k) = 10 + 3k tells us how many loaves Moses will bake based on the kilograms of flour he receives. This means for every kilogram of flour, Moses will bake 33 additional loaves, plus a base amount of 1010 loaves.
  2. Calculating the number of loaves: Calculate the number of loaves Moses will bake with kk kilograms of flour. Using the function N(k)N(k), we find that the number of loaves baked is N(k)=10+3kN(k) = 10 + 3k.
  3. Understanding the relationship between income: Understand the relationship between income and the number of loaves. The function I(x)=6xI(x) = 6x tells us that Moses makes $6\$6 for every loaf of bread he bakes and sells.
  4. Combining the two functions: Combine the two functions to find the expression for income based on kilograms of flour.\newlineWe need to substitute the expression for the number of loaves N(k)N(k) into the income function I(x)I(x). So we replace xx in I(x)I(x) with the expression for N(k)N(k), which is 10+3k10 + 3k.
  5. Performing the substitution: Perform the substitution to find the income function based on kk.I(N(k))=I(10+3k)=6×(10+3k)=60+18k.I(N(k)) = I(10 + 3k) = 6 \times (10 + 3k) = 60 + 18k.
  6. Identifying the correct expression: Identify the correct expression from the given choices.\newlineThe expression we found for Moses's income based on kk kilograms of flour is 60+18k60 + 18k, which corresponds to choice (C).

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