Intermediate Algebra (11th edition)

61.Randall Albritton wants to mix 50 lb of
nuts worth $2 per lb with some nuts
worth $6 per lb to make a mixture worth
$5 per lb. How many pounds of $6 nuts
must he use?

62.Lee Ann Spahr wants to mix tea worth

2¢ per oz with 100 oz of tea worth 5¢

per oz to make a mixture worth 3¢ per

oz. How much 2¢ tea should be used?

SECTION 2.3 Applications of Linear Equations 79

Pounds Cost per Total

of Nuts Pound Cost

Ounces Cost per Total

of Tea Ounce Cost

63.Why is it impossible to mix candy worth $4 per lb and candy worth $5 per lb to obtain a
final mixture worth $6 per lb?

64.Write an equation based on the following problem, solve the equation, and explain why
the problem has no solution:
How much 30% acid should be mixed with 15 L of 50% acid to obtain a mixture that
is 60% acid?

EXERCISES 65 –68

FOR INDIVIDUAL OR GROUP WORK

Consider each problem.

Problem A Jack has $800 invested in two accounts. One pays 5% interest per year and

the other pays 10% interest per year. The amount of yearly interest is the same as he

would get if the entire $800 was invested at 8.75%. How much does he have invested at

each rate?

Problem B Jill has 800 L of acid solution. She obtained it by mixing some 5% acid

with some 10% acid. Her final mixture of 800 L is 8.75% acid. How much of each of

the 5% and 10% solutions did she use to get her final mixture?

In Problem A, let x represent the amount invested at 5% interest, and in Problem B,

let y represent the amount of 5% acid used. Work Exercises 65 – 68 in order.

65. (a)Write an expression in xthat represents the amount of money Jack invested at
    10% in Problem A.
    (b)Write an expression in ythat represents the amount of 10% acid solution Jill
    used in Problem B.


66. (a)Write expressions that represent the amount of interest Jack earns per year at
    5% and at 10%.
    (b)Write expressions that represent the amount of pure acid in Jill’s 5% and 10%
    acid solutions.


67. (a)The sum of the two expressions in part (a) of Exercise 66must equal the total
    amount of interest earned in one year. Write an equation representing this fact.
    (b)The sum of the two expressions in part (b) of Exercise 66must equal the
    amount of pure acid in the final mixture. Write an equation representing this
    fact.


68. (a)Solve Problem A. (b)Solve Problem B.
    (c)Explain the similarities between the processes used in solving Problems A
    and B.

RELATING CONCEPTS