Guess-and-check word problems
Learn with an example
▶️ A team from the college went on a science-and-maths quiz show. The science questions were worth 5 points and the maths questions were worth 6 points. The team answered a total of 8 questions and earned 44 points. How many questions did the team answer in each category?
____ science questions
____ maths questions
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 8.
Guess #1: 6 science questions and 2 maths questions
Find the number of questions:
6 + 2 = 8
Find the total number of points:
(5 × 6) + (6 × 2) = 30 + 12 = 42
The guess is incorrect. Try another guess.
Guess #2: 7 science questions and 1 maths question
Find the number of questions:
7 + 1 = 8
Find the total number of points:
(5 × 7) + (6 × 1) = 35 + 6 = 41
The guess is incorrect. Try another guess.
Guess #3: 4 science questions and 4 maths questions
Find the number of questions:
4 + 4 = 8
Find the total number of points:
(5 × 4) + (6 × 4) = 20 + 24 = 44
The guess is correct. The team answered 4 science questions and 4 maths questions.
▶️ Caleb made fudge brownies and peanut butter brownies. Each batch of fudge brownies makes 5 pans. Each batch of peanut butter brownies makes 3 pans. Caleb made 5 batches and ended up with 21 pans of brownies. How many batches of each type of brownie did he make?
____ batches of fudge brownies
_____ batches of peanut butter brownies
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 5.
Guess #1: 2 batches of fudge brownies and 3 batches of peanut butter brownies
Find the number of batches:
2 + 3 = 5
Find the total pans of brownies:
(5 × 2) + (3 × 3) = 10 + 9 = 19
The guess is incorrect. Try another guess.
Guess #2: 1 batch of fudge brownies and 4 batches of peanut butter brownies
Find the number of batches:
1 + 4 = 5
Find the total pans of brownies:
(5 × 1) + (3 × 4) = 5 + 12 = 17
The guess is incorrect. Try another guess.
Guess #3: 3 batches of fudge brownies and 2 batches of peanut butter brownies
Find the number of batches:
3 + 2 = 5
Find the total pans of brownies:
(5 × 3) + (3 × 2) = 15 + 6 = 21
The guess is correct. Caleb made 3 batches of fudge brownies and 2 batches of peanut butter brownies.
▶️ A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 7 metres long and each piece of plastic pipe was 5 metres long. He bought 6 pieces of pipe. The total length of the pipe was 32 metres. How many pieces of each type of pipe did the plumber buy?
____ pieces of copper pipe
____ pieces of plastic pipe
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 6.
Guess #1: 2 pieces of copper pipe and 4 pieces of plastic pipe
Find the number of pieces of pipe:
2 + 4 = 6
Find the total metres of pipe:
(7 × 2) + (5 × 4) = 14 + 20 = 34
The guess is incorrect. Try another guess.
Guess #2: 4 pieces of copper pipe and 2 pieces of plastic pipe
Find the number of pieces of pipe:
4 + 2 = 6
Find the total metres of pipe:
(7 × 4) + (5 × 2) = 28 + 10 = 38
The guess is incorrect. Try another guess.
Guess #3: 1 piece of copper pipe and 5 pieces of plastic pipe
Find the number of pieces of pipe:
1 + 5 = 6
Find the total metres of pipe:
(7 × 1) + (5 × 5) = 7 + 25 = 32
The guess is correct. The plumber bought 1 piece of copper pipe and 5 pieces of plastic pipe.
Let’s practice! 🖊️
