A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 67 kilograms. A
delivery of 8 large boxes and 3 small boxes has a total weight of 166 kilograms. How much does each type of box weigh?
Weight of each large box: kilogram(s)
Weight of each small box: kilogram(s)

Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 67 kilograms. A
delivery of 8 large boxes and 3 small boxes has a total weight of 166 kilograms. How much does each type of box weigh?
Weight of each large box:

kilogram(s)
Weight of each small box:

kilogram(s)

UpStudy AI · Accepted Answer

**Step 1: Set Up the Equations**

Let $$ L $$ be the weight of one large box (in kilograms) and $$ S $$ be the weight of one small box (in kilograms). The problem gives us the following equations:

1. For 2 large boxes and 5 small boxes weighing 67 kg:
   $$
   2L + 5S = 67
   $$
2. For 8 large boxes and 3 small boxes weighing 166 kg:
   $$
   8L + 3S = 166
   $$

---

**Step 2: Solve by Elimination**

To eliminate one of the variables, we multiply the first equation by 4:
$$
4(2L + 5S) = 4(67) \quad \Longrightarrow \quad 8L + 20S = 268
$$

Now we have:
$$
\begin{aligned}
8L + 20S &= 268 \quad \text{(Equation A)}\
8L + 3S  &= 166 \quad \text{(Equation B)}
\end{aligned}
$$

Subtract Equation B from Equation A:
$$
(8L + 20S) - (8L + 3S) = 268 - 166
$$
$$
8L - 8L + 20S - 3S = 102
$$
$$
17S = 102
$$

Solve for $$ S $$:
$$
S = \frac{102}{17} = 6
$$

---

**Step 3: Solve for $$ L $$**

Substitute $$ S = 6 $$ back into one of the original equations. Using the first equation:
$$
2L + 5(6) = 67
$$
$$
2L + 30 = 67
$$
$$
2L = 67 - 30 = 37
$$
$$
L = \frac{37}{2} = 18.5
$$

---

**Final Answer**

Weight of each large box: $$ 18.5 $$ kilogram(s)  
Weight of each small box: $$ 6 $$ kilogram(s)
Each large box weighs 18.5 kilograms and each small box weighs 6 kilograms.

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