Algebra- QUIZ 3: REPRESENTING PROBLEMS USING A LINEAR SYSTEM

The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100 meters, what is the width of the rectangle?

12 meters

Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim?

15 years old

The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the original number. What is the original number?

39

If t = the tens digit and u = the ones digit, which expression shows the value of interchanging the digits in a two digit number?

10u+t

If b = the rate a boat travels and c = the rate of the current, then which of the following expressions represents the rate of the boat traveling with the current?

b + c

One number is 4 more than another, and their sum is 60. What is the smaller number? If x = the larger number and y = the smaller number, then which of the following systems could be used to solve the problem?

x + y = 60 and x - y = 4

A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.

...

How many gallons of bleach are in x gallons of a 70% bleach solution?

0.7x

A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

3

The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100, find the length and width of the rectangle. If l = length and w = width, which of the following systems could be used to solve the problem?

l = 3w + 2 and 2l + 2w = 100

How much interest is earned on $2,700 in one year if it is invested at 3%?

$81.00

One number is 4 more than another, and their sum is 60. What is the smaller number?

28

$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is $155. How much money was invested at 3% interest?

$4,000

$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is $155. Let x and y represent the two amounts invested. Complete the equation. _____________= 155

0.03x + 0.035y

Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim? If D = dad's age now and J = Jim's age now, which of the following systems could be used to solve the problem?

D = 4J and D + 10 = 2(J + 10) + 20