9.1-9.2 Systems of equations word

problems

I will be able to…• Use systems of equations in 2 variables to model and solve real-life problems

Tickets to the football game are being sold in the main office. On the first day of sales, 50 adult tickets and 40 student tickets were sold totaling $350. On the second day of sales, 20 adult tickets and 60 student tickets were sold totaling $250. How much does an adult ticket cost?Let x = cost of adult ticket and y = cost of student ticket

50x 40y 350

50 adult tickets and 40 student tickets were sold totaling $350

20 adult tickets and 60 student tickets were sold totaling $250 20x 60y 250

5x 4y 35

2x 6y 25

15x 12y 105

4x 12y 50

11x 55 x 5

An adult ticket costs $5.

# 1

#2A

x

y

2x + y = 168

x = 1.5y

63 x 42So 63 - 42 = 21

The perimeter of your neighbor’s rectangular yard is 210 feet. The length is 1 ½ times the width. Find: the width of your neighbor’s lot.

# 2B

x

y

2x + y = 168

x = 1.5y

63 x 42

Using your dimensions of the lot from your previous problem, find the cost of fencing the lot if the yard does not need to be fenced along the house, and panels cost $10 per foot.

63 + 42+42=147

147 x $10 = $1470

A total of $20,000 is invested in two funds paying 6.5% and 8.5% simple interest. The 6.5% investment has a lower risk. The investor wants a yearly interest check of $1600 from the investments. What amount should be invested at each interest rate to meet the requirement of $1600 per year in interest?

#3

x y 20000

.065x .085y 1600

To attain $1600 per year, invest $5000 at 6.5% and $15000 at 8.5%.

CalculatorYou are offered two different jobs selling X-box machines. One

company offers an annual salary of $25000 plus a year-end bonus of 2% of your total sales. The other company offers an annual salary of $20000 plus a year-end bonus of 3% of your total sales. Determine the annual sales required to make the second offer better.

# 4

Next slide

4.

Would have to sell more than 500,000 X-box machines for second salary offer to be better.

Try it…5.

x

y

2x + 2y = 280

y = x – 20

80 x 60 So 80 + 60 = 140

•The perimeter of a rectangular house is 280 feet. Its width is 20 feet less than its length. Find the sum of the dimensions.

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. use "t" for the "tens" digit "u" for the "units" (or "ones") digit.

Keep in mind that the tens digit stands for "ten times this value"

t + u = 7original number: 10t + 1unew number: 10u + 1t (new number) is (old number) increased by (twenty-seven)

10u + 1t = 10t + 1u + 27 25

6.

A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees with a total of $487. The second order was for 6 bushes and 2 trees, and had a total of $232. The bills do not list the per-item price. What was the cost of one tree?

first order: 13b + 4t = 487 second order: 6b + 2t = 232

Bushes cost $23 each; trees cost $47 each.

7.

9.1-9.2 Systems of equations word

problems

I CAN… Use systems of equations in 2 variables to model and solve real-life problems