Math Drills
Elimination Problems
2Word 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
Grade it with your phone
Take a photo of the finished sheet and the answers are checked for you.
Grade with a photoOther versions of this worksheet
Problems and answers on this worksheet
These are the problems in “Various Word Problems”, shown with their answers.
(1)3 pairs of sunglasses and 2 caps cost 460 dollars, and 3 pairs of sunglasses and 5 caps cost 700 dollars. What is the price of 1 pair of sunglasses and 1 cap each? 1 pair of sunglasses □ 1 cap □
Answer: 100dollars, 80dollars
(2)1 backpack and 2 basketballs together cost 220 dollars. 2 backpacks and 3 basketballs together cost 380 dollars. How much do 1 backpack and 1 basketball each cost? 1 backpack □ 1 basketball □
Answer: 100dollars, 60dollars
(3)1 backpack costs 50 dollars more than 1 cap. Buying 1 backpack and 1 cap together costs 230 dollars. How much does each cost? 1 backpack □ 1 cap □
Answer: 140dollars, 90dollars
(4)1 set of A contains 2 backpacks and 3 caps for 270 dollars, and 1 set of B contains 3 backpacks and 1 cap for 300 dollars. How much do 1 backpack and 1 cap cost, each? 1 backpack □ 1 cap □
Answer: 90dollars, 30dollars
(5)1 water bottle and 1 backpack together cost 135 dollars. 1 backpack and 1 sneaker together cost 170 dollars. 1 sneaker and 1 water bottle together cost 155 dollars. How much does 1 of each of the 3 items cost? water bottle □ backpack □ sneaker □
Answer: 60dollars, 75dollars, 95dollars
