Round the quotient up to carry the remainder

3.OA.A.33.MD.A.2 · adapt · grade 3

Archetype: Divisibility and Remainder Reasoning · step in a 8-type progression

A warehouse needs to load $60$ sacks of rice onto trucks, where each sack weighs $180\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 60 sacks of rice, each weighing 180 lb. A truck can carry at most 1 ton (2000 lb). Find the least number of trucks needed.

Givens

There are 60 sacks of rice.
Each sack weighs 180 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 60 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 60 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 180 lb sacks fit under 2000 lb per truck, then divide the 60 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 180 lb and the limit is 2000 lb. Since 11 x 180 = 1980 lb (under the limit) but 12 x 180 = 2160 lb (over the limit), one truck can carry at most 11 sacks.

11 \times 180 = 1980 \le 2000,\quad 12 \times 180 = 2160 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 11 sacks per truck, 60 sacks need 60 divided by 11, which is 5 trucks carrying 55 sacks with 5 sacks left over.

60 \div 11 = 5\ \text{R}\ 5

Five full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 5 leftover sacks still need a truck, so add 1 more: 5 + 1 = 6 trucks.

5 + 1 = 6\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 6 trucks

Review

Six trucks can carry up to 6 x 11 = 66 sacks, which is enough for 60; five trucks carry only 55, which is too few. So 6 is the least number.

Guess and check by total weight (tool 6): 60 sacks weigh 60 x 180 = 10800 lb; 10800 / 2000 = 5.4, which rounds up to 6 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!