Problem
Fixed sum: one side falls, other rises
Wujin bought a mix of 500-won snacks and 700-won juice boxes. Altogether he bought 15 items and paid 8300 won. We need to find how many of each he bought.
Operations
Your answer
How to solve
Strategy Guess and Check — Because the number of items is fixed at 15, we can guess one starting case (say, all snacks) and then check the total. The total sum of items stays at 15, so each time we trade one snack for one juice box the count of items doesn't change but the price climbs by a steady 200 won. Spotting that pattern lets us jump straight to the right answer instead of testing every case, and a short list confirms it. This keeps the reasoning concrete for a young learner instead of jumping to algebra.
1STEP 1
Start with an easy guess: all 15 are snacks
Imagine all 15 items were snacks. Then the cost would be 15 groups of 500 won.
15 × 500 = 7500
Trying the simplest extreme case first gives a number we can compare against the real total.
4.NBT.B.5Guess And Check2STEP 2
See how far off the guess is
Wujin actually paid 8300 won, which is more than 7500 won. Find the gap that the juice boxes must make up.
8300 - 7500 = 800
The leftover 800 won has to come from swapping some snacks for the pricier juice boxes.
4.NBT.B.4Guess And Check3STEP 3
Find the steady jump per swap (the pattern)
Each swap keeps the count at 15 but lifts the bill by 700 - 500 = 200 won.
700 - 500 = 200
Because every swap adds the same 200 won, the extra cost grows in equal steps we can count.
5.OA.A.2Look For A PatternSwapping one snack for one juice box leaves the item count at 15 and raises the total by exactly 200 won.
Why?
A swap takes one item out and puts one item in, so the count loses one and gains one and ends up right where it started.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Nothing else in the basket is touched, so the total moves only by the gap between the two prices, 700 won against 500 won.
Why?
The total is every item's price added together, so replacing one price with another shifts the total by exactly that difference.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
4STEP 4
Count how many swaps reach the gap
Divide the 800-won gap by the 200-won step to find the number of juice boxes.
800 ÷ 200 = 4
If each swap is worth 200 won, then 4 swaps give exactly the 800 won we needed.
4.OA.A.3Look For A Pattern5STEP 5
Find the snacks and confirm with a quick list
Four juice boxes leave 15 - 4 = 11 snacks, and 5500 + 2800 = 8300 checks out.
15 - 4 = 11, 11 × 500 + 4 × 700 = 5500 + 2800 = 8300
Listing both counts and adding the money back confirms the answer fits all the clues.
4.OA.A.3Make A Systematic ListAnswer
11 snacks and 4 juice boxes
The two counts add to 15 items (11 + 4 = 15) and the money adds to 8300 won (5500 + 2800 = 8300), so both totals match. Since juice boxes cost a little more, having fewer of them (4) than snacks (11) makes sense for a total only a bit above the all-snacks price of 7500 won.
Takeaway
When the number of things is fixed, swapping a cheap one for a pricey one keeps the count the same but bumps the cost by a steady amount you can count.
- Start with an easy guess: all 15 are snacks
- See how far off the guess is
- Find the steady jump per swap (the pattern)
- Count how many swaps reach the gap
- Find the snacks and confirm with a quick list
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested