# Systems of equations word problems

## Presentation on theme: "Systems of equations word problems"— Presentation transcript:

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

Let x = cost of adult ticket and y = cost of student ticket
# 1 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 50 adult tickets and 40 student tickets were sold totaling \$350 20 adult tickets and 60 student tickets were sold totaling \$250 An adult ticket costs \$5.

#2A 2x + y = 168 x = 1.5y x 63 x 42 So = 21 y 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 2x + y = 168 x = 1.5y 63 x 42 =147 147 x \$10 = \$1470 x y 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.

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

# 4 Calculator You 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. Next slide

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

5. Try it… The perimeter of a rectangular house is 280 feet. Its width is 20 feet less than its length. Find the sum of the dimensions. 2x + 2y = 280 x y = x – 20 y 80 x 60 So = 140

6. 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 = 7 original number: 10t + 1u new number: 10u + 1t (new number) is (old number) increased by (twenty-seven) 10u + 1t = 10t + 1u + 27 25

Bushes cost \$23 each; trees cost \$47 each. first order: 13b + 4t = 487
7. 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.

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