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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.