The idea in brief. Equal groups can be removed from both totals or replaced by another group of equal value. Cancel only the same quantity on both sides. Different items need not have the same value. In the lesson. In the last lesson, two changes made a difference between two equal amounts. Today, we will compare two purchases by matching the same items in both. Cross out the items that both purchases have. The extra items make the extra cost.
Lesson video, with the working
Equal groups in two totals
5 min 34 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
A beach stall charges the same prices on both visits. Mei buys 2 buckets and 3 scoops for $24 on one visit. On another visit, Mei buys 4 buckets and 3 scoops for $36. How much does one bucket cost?
Extra cost = $36 − $24 = $12
Extra buckets = 4 − 2 = 2
Cost of one bucket = $12 ÷ 2 = $6
Ans: $6
Example 1 of 2
A beach stall charges the same prices on both visits. Siti buys 1 bucket and 2 scoops for $17 on one visit. On another visit, Siti buys 4 buckets and 2 scoops for $38. How much does one bucket cost?
Extra cost = $38 − $17 = $21
Extra buckets = 4 − 1 = 3
Cost of one bucket = $21 ÷ 3 = $7
Ans: $7
Example 2 of 2
A beach stall charges the same prices on both visits. Bala buys 2 buckets and 2 scoops for $16 on one visit. On another visit, Bala buys 5 buckets and 2 scoops for $31. How much does one scoop cost?
Extra cost = $31 − $16 = $15
Extra buckets = 5 − 2 = 3
Cost of one bucket = $15 ÷ 3 = $5
Cost of 2 buckets = $5 × 2 = $10
Cost of 2 scoops = $16 − $10 = $6
Cost of one scoop = $6 ÷ 2 = $3
Ans: $3
How to solve it
Draw each visit in its own row, with its items and its total cost.
Match the items both visits have, and cross them out. They cost the same on both visits.
Only the extra items on the second visit are left. Subtract the totals for the extra cost: 36 minus 24 is 12.
Subtract the items to see how many are extra: 4 minus 2 is 2 extra buckets.
Share the extra cost equally: 12 divided by 2 is 6, so one bucket costs 6 dollars.
For the other item, go back to one visit: Bala’s 2 buckets cost 10 dollars, so 16 minus 10 is 6 dollars for 2 scoops.
Cross out the items that both purchases have. The extra items make the extra cost.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its solution film.
Question 1 of 8 · Basic · free to tryA shop charges the same prices on both visits. On one visit, 2 notebooks and…A shop charges the same prices…
A shop charges the same prices on both visits. On one visit, 2 notebooks and 3 folders cost $51. On another visit, 4 notebooks and 3 folders cost $63. How much does one notebook cost?
How do P3 elimination word problems find one price from two purchases?
Here your child compares two totals that share some of the same items.
What your child learns here
Here your child compares two totals that share some of the same items. Crossing out what matches leaves only the extra items and the extra cost. The page applies Primary 3 subtraction, division within the tables and money to this kind of word problem.
Line up two purchases in two rows, with the same items under each other.
Cross out the items that appear in both, so the difference in cost belongs only to the extra items.
Divide the extra cost by the number of extra items to find one price.
Use that price to work back to the price of the other item.
Swap one item for an equal group of another when the question says they have equal value.
Does the answer make sense?
One notebook, folder or brush must cost less than any total it is part of, and the gap between two totals must equal the cost of the extra items alone. With both prices or masses found, your child can rebuild both purchases or both scales and match each total.
How to practise these questions
The Basic questions practise lining up the two totals and finding what the difference between them pays for. The Intermediate questions add totals where the groups must be matched before comparing. The Challenge question asks your child to scale one total before the extra items can be compared. If a two-totals question stalls, watch the solution film for it and return to it later from Revision.
Questions parents ask
What is the elimination method in P3 maths? Two purchases share some identical items. Crossing out what they share leaves the extra items, and the extra cost belongs to them alone. Dividing the extra cost by the number of extra items gives one price.
Is elimination in the Primary 3 syllabus? The P3 syllabus lists adding and subtracting money, and multiplying and dividing within the tables. Comparing two purchases applies those skills to a word problem; the syllabus does not name the method itself.
What is replacement in these questions? When the question says one item has the same value as a group of others, the item can be swapped for that group. After the swap, both sides are written in the same kind of item and can be compared.
