Equal groups in two totals

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. A beach stall charges the same prices on both visits. Mei buys 2 buckets and 3 scoops for 24 dollars on one visit. On another visit, Mei buys 4 buckets and 3 scoops for 36 dollars. How much does one bucket cost? We draw each visit in its own row. The first visit has 2 buckets and 3 scoops. The first purchase costs 24 dollars. The second visit has 4 buckets and 3 scoops. The second purchase costs 36 dollars. We need the price of one bucket. Both visits have 2 buckets, so we match them. Both visits have 3 scoops too, so we match them. They cost the same on both visits, so we cross them out. Only the extra buckets on the second visit are left. They make the extra cost. 36 dollars minus 24 dollars is 12 dollars. 4 minus 2 is 2 extra buckets. The 2 extra buckets share the 12 dollars equally. 12 dollars divided by 2 is 6 dollars. So one bucket costs 6 dollars.

A beach stall charges the same prices on both visits. Siti buys 1 bucket and 2 scoops for 17 dollars on one visit. On another visit, Siti buys 4 buckets and 2 scoops for 38 dollars. How much does one bucket cost? Try it first. Pause if you like. The first visit has 1 bucket and 2 scoops. The first purchase costs 17 dollars. The second visit has 4 buckets and 2 scoops. The second purchase costs 38 dollars. Both visits have 1 bucket and 2 scoops, so we match them. They cost the same, so we cross them out. Only the extra buckets on the second visit are left. They make the extra cost. 38 dollars minus 17 dollars is 21 dollars. 4 minus 1 is 3 extra buckets. 21 dollars divided by 3 is 7 dollars. So one bucket costs 7 dollars.

A beach stall charges the same prices on both visits. Bala buys 2 buckets and 2 scoops for 16 dollars on one visit. On another visit, Bala buys 5 buckets and 2 scoops for 31 dollars. How much does one scoop cost? Try it first. Pause if you like. The first visit has 2 buckets and 2 scoops. The first purchase costs 16 dollars. The second visit has 5 buckets and 2 scoops. The second purchase costs 31 dollars. We need the price of one scoop. Both visits have 2 buckets and 2 scoops, so we match them. They cost the same, so we cross them out. Only the extra buckets on the second visit are left. They make the extra cost. 31 dollars minus 16 dollars is 15 dollars. 5 minus 2 is 3 extra buckets. 15 dollars divided by 3 is 5 dollars. We still pay for crossed-out items. On the first visit, Bala's 2 buckets cost 5 dollars each. 5 dollars times 2 is 10 dollars. The rest of the 16 dollars pays for the 2 scoops. 16 dollars minus 10 dollars is 6 dollars. 6 dollars divided by 2 is 3 dollars. So one scoop costs 3 dollars. Cross out the items that both purchases have. The extra items make the extra cost.