1.You invested a total of $10,000 at 4 1 2 % and 5% simple interest. During one

Question

1.You invested a total of $10,000 at 4 1 2 % and 5% simple interest. During one year, the two accounts earned $490. How much did you invest in each account? (i) 4 1/ 2 % interest $ _________ (ii) 5% interest $_______

B.Write a mathematical model for the problem and solve. One positive number is 4 times another number. The difference between the two numbers is 93. Find the numbers. (Enter your answers as a comma-separated list.)

C. Write an algebraic expression for the verbal description. The total cost of producing x units for which the fixed costs are $2800 and the cost per unit is $35

$____

D. Translate the statement into an algebraic expression or equation. The cost in dollars of forty percent of the list price L

$__________

E. Translate the statement into an algebraic expression or equation.The percent p of 664 that is represented by the number N

p =___________ %

2. A rectangular room is 1.5 times as long as it is wide, and its perimeter is 40 meters.

(a) Draw a diagram that gives a visual representation of the problem. Let l represent the length and let w represent the width.

(b) Write l in terms of w.
l =  

Write an equation for the perimeter P in terms of w.

P =   

Explanation / Answer

1. 1.You invested a total of $10,000 at 4 1 2 % and 5% simple interest. During one year, the two accounts earned $490. How much did you invest in each account?

Let x $ be invested in at 4.5 % and 10000 -x be invested at 5% siple interest

So, Interest on 4.5% = 0.045x

Interest on 5% = (10,000 -x)0.05 = 500 -0.05x

Interest in 1 year = $ 490

So, 0.045x + 500 -0.05x = 490

-0.005x + 500 = 490

x = $2000 at 4.5^ interest

10000- x = $ 8000 at 5% interest

2) B.Write a mathematical model for the problem and solve. One positive number is 4 times another number. The difference between the two numbers is 93. Find the numbers

Let one number be x , then other number = 4x

difference between the two numbers is 93 : 4x -x = 93

3x = 93 ; x = 93/3 = 31

x = 31 and 4x = 4*31 = 124

The two numbers are 31 and 124

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