A boat must carry aluminum pieces for a construction project that weigh, in total, no more than 50,000 kilograms (kg). Each aluminum piece is either a beam, which weighs 100kg, or a connector plate, which weighs 2kg. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams, b(c), as a function of the number of connector plates, c ? Choose 1 answer: (A) b(c)=500-0.02 c (B) b(c)=25,000-50 c (c) b(c)=50,000-100 c (D) b(c)=50,000-2c

Identify Maximum Weight: Identify the total maximum weight the boat can carry and the weights of individual items. The boat can carry a maximum of 50,000 kg. Each beam weighs 100 kg, and each connector plate weighs 2 kg.Set Up Equation: Set up an equation for the total weight of beams and connector plates. Let b be the number of beams and c be the number of connector plates. The total weight is the sum of the weight of the beams and the weight of the connector plates, which should be no more than 50,000 kg. So, the equation is 100b + 2c ≤ 50,000.Solve for b: Solve the equation for b as a function of c. To express b as a function of c, we need to isolate b on one side of the equation. We do this by subtracting 2c from both sides and then dividing by 100: 100b + 2c = 50,000 100b = 50,000 - 2c b(c) = (50,000 - 2c) / 100Simplify Function: Simplify the function b(c). Divide both terms on the right-hand side by 100 to simplify the function: b(c) = 50,000/100 - 2c/100 b(c) = 500 - 0.02c

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A boat must carry aluminum pieces for a construction project that weigh, in total, no more than 50,000 kilograms (kg). Each aluminum piece is either a beam, which weighs
100kg, or a connector plate, which weighs
2kg. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams,
b(c), as a function of the number of connector plates,
c ?
Choose 1 answer:
(A)
b(c)=500-0.02 c
(B)
b(c)=25,000-50 c
(c)
b(c)=50,000-100 c
(D)
b(c)=50,000-2c

A boat must carry aluminum pieces for a construction project that weigh, in total, no more than $50$ , $000$ kilograms $(\mathrm{kg})$ . Each aluminum piece is either a beam, which weighs $100 \mathrm{~kg}$ , or a connector plate, which weighs $2 \mathrm{~kg}$ . If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams, $b(c)$ , as a function of the number of connector plates, $c$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $b(c)=500-0.02 c$ $\newline$ (B) $b(c)=25,000-50 c$ $\newline$ (C) $b(c)=50,000-100 c$ $\newline$ (D) $b(c)=50,000-2 c$

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Grade 8

Write linear functions: word problems

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Q. A boat must carry aluminum pieces for a construction project that weigh, in total, no more than

50

000

kilograms

(\mathrm{kg})

. Each aluminum piece is either a beam, which weighs

100 \mathrm{~kg}

, or a connector plate, which weighs

2 \mathrm{~kg}

. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams,

b(c)

, as a function of the number of connector plates,

c

\newline

Choose

1

answer:

\newline

(A)

b(c)=500-0.02 c

\newline

(B)

b(c)=25,000-50 c

\newline

(C)

b(c)=50,000-100 c

\newline

(D)

b(c)=50,000-2 c

Identify Maximum Weight: Identify the total maximum weight the boat can carry and the weights of individual items. $\newline$ The boat can carry a maximum of $50,000$ kg. Each beam weighs $100$ kg, and each connector plate weighs $2$ kg.
Set Up Equation: Set up an equation for the total weight of beams and connector plates. Let $b$ be the number of beams and $c$ be the number of connector plates. The total weight is the sum of the weight of the beams and the weight of the connector plates, which should be no more than $50,000$ kg. So, the equation is $100b + 2c \leq 50,000$ .
Solve for b: Solve the equation for b as a function of c. $\newline$ To express $b$ as a function of $c$ , we need to isolate $b$ on one side of the equation. We do this by subtracting $2c$ from both sides and then dividing by $100$ : $\newline$ $100b + 2c = 50,000$ $\newline$ $100b = 50,000 - 2c$ $\newline$ $b(c) = \frac{50,000 - 2c}{100}$
Simplify Function: Simplify the function $b(c)$ . $\newline$ Divide both terms on the right-hand side by $100$ to simplify the function: $\newline$ $b(c) = \frac{50,000}{100} - \frac{2c}{100}$ $\newline$ $b(c) = 500 - 0.02c$