Math Drills
Elimination Problems
1Word Problems
What this worksheet covers
Grade 6 (Elementary School) / Various Word Problems / Elimination Problems
The price of each single item is worked out from the prices of two ways of buying, in word problems. Five ways of eliminating are tried: subtracting straight where the counts match, doubling one expression before eliminating, producing both from a difference and a total, two expressions with different combinations in a set, and using the totals of each pair among three items.
What gets doubled is the whole expression, so the count of items and the total price both grow by the same multiplier. A paper that doubled only the count of items and left the money on the right as it was has moved only one side within the single line it rewrote.
Crane and Turtle Problems went forward by supposing everything to be one kind, whereas here two expressions are set side by side and what they share is eliminated. One of those two comes in the form of an unchanging difference in years, in Age Problems.
- Subtracting Directly to Eliminate1 question
- Multiplying Then Eliminating1 question
- Using the Difference1 question
- Buying in Sets1 question
- Three Items1 question
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Problems and answers on this worksheet
These are the problems in “Various Word Problems”, shown with their answers.
(1)2 backpacks and 3 pairs of shoes cost 580 dollars, and 2 backpacks and 6 pairs of shoes cost 880 dollars. What is the price of 1 backpack and 1 pair of shoes each? 1 backpack □ 1 pair of shoes □
Answer: 140dollars, 100dollars
(2)1 backpack and 3 basketballs together cost 240 dollars. 2 backpacks and 2 basketballs together cost 280 dollars. How much do 1 backpack and 1 basketball each cost? 1 backpack □ 1 basketball □
Answer: 90dollars, 50dollars
(3)1 backpack costs 40 dollars more than 1 cap. Buying 1 backpack and 1 cap together costs 200 dollars. How much does each cost? 1 backpack □ 1 cap □
Answer: 120dollars, 80dollars
(4)1 set of A contains 2 backpacks and 3 caps for 280 dollars, and 1 set of B contains 3 backpacks and 1 cap for 280 dollars. How much do 1 backpack and 1 cap cost, each? 1 backpack □ 1 cap □
Answer: 80dollars, 40dollars
(5)1 water bottle and 1 backpack together cost 150 dollars. 1 backpack and 1 sneaker together cost 170 dollars. 1 sneaker and 1 water bottle together cost 160 dollars. How much does 1 of each of the 3 items cost? water bottle □ backpack □ sneaker □
Answer: 70dollars, 80dollars, 90dollars
