Math 1 January 21, 2021

Math 1

January 21, 2021

Example 1

The larger of two numbers is 5 more than twice the smaller. If the smaller is subtracted from the larger, the result is 12. Find the numbers.

Example 2

Two taxi companies charge different rates.

Metro Taxi: $3.00 for the first mile and $2.50 for each additional mile

City Taxi: $5.00 for the first mile and $2.25 for each additional mile

When will the two taxi companies cost the same? Describe a situation in which it would make more sense to use Metro Taxi. Then describe a different situation in which it would make more sense to use City Taxi. 

Example 3

A light plane flew from its home base to an airport 255 miles away. With a head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find the average airspeed of the plane and the average windspeed.

Example 4

 $6x+9y=24$  
 $7x-2y=3$  

Example 5

The school that Brenda goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 9 adult tickets and 2 child tickets for a total of $103. The school took in $137 on the second day by selling 3 adult tickets and 10 child tickets. Find the

price of an adult ticket and the price of a child ticket.

Fill in the Blanks

Bill wants to order new jerseys for his baseball team. He sees the following advertisements for two printing companies, ‘PRINT IT’ and ‘TOP PRINT’. What is the maximum number of jerseys Bill can purchase from 'PRINT IT' for it to remain the best deal?

Fill in the Blanks

A bicycle store costs $2,400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $y=3x-10$  
 $y=2x-5$  

• no solution

• one solution

• infinitely many solutions

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $x=-2y+1$  
 $x=y-5$  

• no solution

• one solution

• infinitely many solutions

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $6x-3y=6$  
 $y=2x+5$  

• no solution

• one solution

• infinitely many solutions

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $y=2x$  
 $7x-y=15$  

• no solution

• one solution

• infinitely many solutions

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $4x+7y=3$  
 $4x+7y=5$  

• no solution

• one solution

• infinitely many solutions

Multiple Choice

Tell whether the system has no solution, one solution or infinitely many solutions.

 $x+3y=11$  
 $2x+3y=4$  

• no solution

• one solution

• infinitely many solutions

Fill in the Blanks

Solve each system by substitution. Write your answers:
(x,y) or x,y
I = infinite
NS = no solution

 $4x+8y=4$  
 $y=4x+5$  

Multiple Choice

This table shows a data set. Which approximate linear equation represents the data set?

• $y=20.5x+20.5$

• $y=17.9x+23.5$

• $y=16.3x+30.2$

• $y=12.4x+46.4$

Fill in the Blanks

Solve the equation. Write both answers: smaller number, larger number

ex. (-1,7) or -1,7

 $-9+5\left|-4x+5\right|=96$  

Fill in the Blanks

John’s mother is three less than four times John’s age. Their combined age is 37. What is John’s age?

Fill in the Blanks

Two different fitness center charge a one-time membership fee, plus a monthly charge to use the facilities. Fitness center A charges a membership fee of $100, plus $45 per month. The table shows the cost of fitness center B after a certain number of months of use. What is the difference between the membership fees at the two fitness centers?

Fill in the Blanks

Simplify. Your answer should only contain positive exponents. Use ^ for exponents. Write answers in alphabetical order.

 $\frac{\left(2y^{-2}\right)^3\times\left(2x^3y^2\right)^{-2}}{\left(x^{-3}y^0\right)^{-3}}$