Fix the mistake: Concentration Problems

Concentration Problems ① Calculating the Concentration of Salt Water

“The concentration of salt water” is an important topic that frequently appears in junior high school entrance examinations.
Be sure to learn the relationship between salt, water, and salt water, as well as the formula for finding concentration.

What You Will Learn

Formula for finding concentration (be sure to memorize it):
　Concentration (%) ＝ Weight of salt ÷ Weight of salt water × 100
Other relationships:
　Weight of salt water ＝ Weight of salt ＋ Weight of water
　Weight of salt ＝ Weight of salt water × Concentration ÷ 100

Example Problem
20 g of salt is dissolved in 380 g of water. What is the concentration of this salt water? Also, find the weight of salt contained in 250 g of 8% salt water.

Solution:
① Find the total weight of the salt water.
　Weight of salt water ＝ 380 ＋ 20 ＝ 400g
② Calculate the concentration.
　Concentration ＝ 20 ÷ 400 × 100 ＝ 5%

③ The salt contained in 250 g of 8% salt water is:
　250 × 8 ÷ 100 ＝ 20g

Key Points

Remember
  • The “weight of salt water” includes not only the weight of the water but also the weight of the salt.
  • Remember that adding salt also increases the total weight of the salt water.
  • When only the water evaporates, the weight of the salt does not change; only the weights of the water and salt water decrease.

Practice Problems

  1. 30 g of salt is dissolved in 270 g of water. What is the concentration?
  2. How many grams of salt are contained in 500 g of 12% salt water?
  3. 50 g of water is evaporated from 300 g of 6% salt water. What will the concentration be?

Answers and Explanations

  1. Answer: Concentration = 10%
    Explanation: Weight of salt water = 270 + 30 = 300g. Concentration = 30 ÷ 300 × 100 = 10%. Remember that the weight of salt water is “the weight of water＋the weight of salt.”
  2. Answer: Weight of salt = 60g
    Explanation: Salt = Weight of salt water × Concentration ÷ 100 = 500 × 12 ÷ 100 = 60g.
  3. Answer: Concentration = 7.2%
    Explanation: Salt contained in the original salt water = 300 × 0.06 = 18g. When 50g of water evaporates, the weight of the salt water becomes 300 − 50 = 250g (the weight of the salt does not change). New concentration = 18 ÷ 250 × 100 = 7.2%.

Math (Junior High Entrance Exam): related lessons