Math 1; 25 January

Math 1

January 25, 2021

Example 1

20 lbs. of mixed nuts containing 25%

peanuts were mixed with 15 lbs. of

another kind of mixed nuts that contain 60% peanuts. Peanuts are what percent of the new mixture?

Example 2

A metal alloy weighing 1 lb. and

containing 30% gold is melted and mixed with 4 lb. of pure gold. What percent of the resulting alloy is gold?

Example 3

For his birthday party Sam mixed

together 2 gal. of Brand A fruit punch and 3 gal. of Brand B. Brand A contains 10% fruit juice and Brand B contains 20% fruit juice. What percent of the mixture is fruit juice?

Example 4

4 qt. of a 42% saline solution was mixed with 3 qt. of pure water. Find the concentration of the new mixture.

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3 yd³ of sand was mixed into 9 yd³ of soil containing 48% sand. What is the sand content of the mixture?

Example 5

 $y\ge\frac{1}{3}x-1$  

Example 6

 $y<-\frac{3}{2}x+1$  

Example 7

 $y\le\frac{5}{3}x$  

Example 8

 $y>-\frac{8}{5}x+4$  

Multiple Choice

What is the equation of the linear inequality in the graph?

• $y\ge3x+2$

• $y\le3x+2$

• $y>3x+2$

• $y<3x+2$

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One line passes  $\left(1,6\right)$  and  $\left(3,0\right)$ . A second line passes through the points  $\left(4,4\right)$   and  $\left(2,8\right)$  . At what point do the two lines intersect?

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

 $y=5x+2$  
 $15x-3y=6$  

Multiple Choice

The table below shows the number of minutes several students spend watching television each night and their math grades. Using a linear model, what is the meaning of the slope?

• A student’s math grade increases approximately 3 points for every 10 minutes of watching television.

• A student’s math grade decreases approximately 3 points for every 10 minutes of watching television.

• A student watches approximately 3 minutes less television for every 10 points gained in their math grade.

• A student watches approximately 3 minutes more television for every 10 points gained in their math grade.

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

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

 $-1-3\left|-8x-1\right|=-94$  

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Solve the equation for x. If x equals a number, write the number, if not:
I = infinite
NS = no solution

 $5\left(4x-3\right)+10=-5\left(1-4x\right)$  

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

 $\frac{\left(2m^2n^3\times m^0\right)^2}{m^{-4}n^{-3}}$  

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Two plumbing companies charge a flat fee, plus an additional cost per hour of service. Martin's plumbing uses the equation

 $y=40x+85$  to determine the total cost of providing x hours of service to a customer. The table shows the total cost to use Alex's Plumbing for different numbers of hours of service. What is the difference in the cost per hour charged by the two companies?

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The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 14 vans and 9 buses with 468 students. High School B rented and filled 7 vans and 6 buses with 270 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

(van, bus)

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A boat traveled 231 miles downstream and back. The trip downstream took 11 hours. The trip back took 77 hours. Find the speed of the boat in still water and the speed of the current.

(boat, current)

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A container ship left the Azores at the same time as a cruise ship. The vessels traveled in opposite directions. The cruise ship traveled at a speed of 30 km/h. After 14 hours they were 770 km apart. How fast did the container ship travel? Just write the number.

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The combined weight of a puppy and its mother is 47 pounds. The mother weighs 8 pounds less than 4 times the weight of the puppy. How much does the puppy weigh?