1. How many ounces of a 7% acid solution and how many ounces of a 23% solution m
ID: 2971175 • Letter: 1
Question
1. How many ounces of a 7% acid solution and how many ounces of a 23% solution must be mixed to obtain 20 ounces of a 17% acid solution?
A. define the variables
B. make a table
C. write an equation and solve the equation
D. respond in a complete sentence
2. Ann counted her money in her piggy bank. She had 63 coins in dimes and quarters. She had a total of $11.55. How many of each type did she have?
A. Define the variables
B. Make a table
C. Write an equation and solve the equation
D. How many $10 bills and how many $20 bills did Ann have in her piggy bank? Respond with a complete sentence.
3. An investment of $20,000 earned a net income of $1,250 in one year. Part of the investment was in bonds and earned income at a rate of 7%. The rest of the investment was in a savings account that earned income at a rate of 4%. How much was invested in bonds and how much in the savings account?
A. Define the variables
B. Make a table
C. Write an equation and solve the equation
D. How much was invested in bonds and how much was invested in the savings account? Respond with a complete sentence.
Explanation / Answer
1.
Let 'x' ounces of 7% acid solution contains -> 0.07x acid
=> '20 - x' ounces of 23% acid solution contains -> 0.23(20 - x) acid
(as there is 20 ounces in total)
20 ounces of a 17% acid solution contains 20*0.17 = 3.4 ounces acid.
=> 0.07x + 0.23(20 - x) = 3.4
=>4.6-3.4 = .16x
=>x = 5 ounces
20 -x = 15 ounces
=>20 ounces of a 17% acid solution has 5 ounces 7% acid solution and 15 ounces 23% acid solution.
2.
Let 'x' number of dimes
As there are 63 coins in total => (63-x) quarters
1 dime = 10 cents = 0.1 dollars
1 quarter = 25 cents = 0.25 dollars
=> Net worth = 0.1x + 0.25(63 - x) = 11.55
=>0.15x = 15.75 - 11.55 = 4.2
=> x = 4.20/0.15 = 28 dimes
63 -x = 63-28 = 35 quarters
=> She has 28 dimes and 35 quarters.
3.
Let 'x' amount in bonds
As we have total investment of 20,000 => (20000 - x) in savings
Net income through bonds/year = 0.07x (Interest * Amount)
Net income through savings/year = 0.04(20000 - x)
=>Net income/year = 0.04(20000 - x) + 0.07x = 1250
=>800 + 0.03x = 1250
=> 0.03x = 450 => x =450/0.03 =15000 Bonds
=>20000 - x = 5000 Savings
=>An investment of $20,000 was spent in the form of 15000 bonds and 5000 savings.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.