In saltwater problems, set up equations using the amount of salt. Amount of salt＝concentration×total amount.
Example ①
You want to mix 5% saltwater and 10% saltwater to make 600 g of 8% saltwater. How many grams of each should be mixed?
Solution: Let the amount of 5% saltwater be x g and the amount of 10% saltwater be y g.
{ x+y=600、0.05x+0.10y=0.08×600=48。
Equation 2 ×100: 5x+10y=4800 → x+2y=960. From ①, x=600−y → substitute: 600−y+2y=960→y=360,x=240。
240g of 5% saltwater and 360g of 10% saltwater
You want to mix 5% saltwater and 10% saltwater to make 600 g of 8% saltwater. How many grams of each should be mixed?
Solution: Let the amount of 5% saltwater be x g and the amount of 10% saltwater be y g.
{ x+y=600、0.05x+0.10y=0.08×600=48。
Equation 2 ×100: 5x+10y=4800 → x+2y=960. From ①, x=600−y → substitute: 600−y+2y=960→y=360,x=240。
240g of 5% saltwater and 360g of 10% saltwater
Key Points
- Set up equations using the amount of salt: concentration(%)÷100 × total amount
- Set up two equations for the total amount and the amount of salt
- Since concentration equations contain decimals, multiply by 100 to make integers
Practice Problem
- You want to mix 4% saltwater and 10% saltwater to make 300g of 6% saltwater. How many grams of each should be mixed?
Answer and Explanation
- Answer:200g of 4% saltwater and 100g of 10% saltwater. { x+y=300、4x+10y=1800. ①×4→4x+4y=1200. Subtracting gives 6y=600→y=100,x=200。