Problem
Concentration is salt over solution
Salt is added to salt water of known concentration. We need the new concentration.
Ratios
Your answer
How to solve
Strategy Identify Subproblems — Concentration is salt over solution, and pouring salt in changes both numbers. The usual slip is to change only the top. Work out both new amounts before dividing.
1STEP 1
Find how much salt is there to start
A concentration of 20% means one fifth of the salt water is salt.
180 × 0.2 = 36
There is 36 g of salt at first.
6.RP.A.3Analyze The Units2STEP 2
Update both amounts
Adding 20 g of salt raises the salt to 56 g, and it also raises the total salt water to 200 g.
36 + 20 = 56, 180 + 20 = 200
Both the top and the bottom changed.
7.RP.A.3Identify SubproblemsAdding salt raises both the salt and the salt water.
Why?
Salt water is the salt together with the water, so anything poured into it counts once in the salt and once in the total.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Work out the new concentration
Divide the new salt by the new salt water and write it as a percent.
56 ÷ 200 = 0.28
The new concentration is 28%.
7.RP.A.3Organize Information In More WaysAnswer
28%
Check it: 28% of 200 g is 56 g of salt, which is the 36 that was there plus the 20 added.
Takeaway
Pouring something in changes both the part and the whole -- update both before dividing.
- Find how much salt is there to start
- Update both amounts
- Work out the new concentration