Lesson 5

Math 1

January 27, 2021

Example 1

A metal alloy weighing 12 kg and

containing 45% platinum is melted and mixed with 8 kg of a different alloy which contains 10% platinum. What percent of the resulting alloy is platinum?

Example 2

10 kg of fruit salad was made by

combining 8 kg of sliced peaches which cost $8/kg with 2 kg of sliced bananas which cost $3/kg. Find the cost per kg of the mixture.

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An alcohol solution was made by mixing 2 gal. of a 90% alcohol solution and 1 gal. of a 45% alcohol solution. What is the concentration of the mixture?

Example 3

How many mg of a metal containing 70% nickel must be combined with 2 mg of pure nickel to form an alloy containing 75% nickel?

Example 4

How many gal. of a 15% acid solution must be mixed with 4 gal. of a 75% acid solution to make a 35% solution?

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Kim wants to make a 12% acid solution. She has already poured 1 fl. oz. of a 40% acid solution into a beaker. How many fl. oz. of a 5% acid solution must she add to this to create the desired mixture?

https://youtu.be/bknKLAnkIRo

Example 5

 $y\ge-\frac{9}{2}x-5$  

Example 6

 $y\le-3x+4$  

Example 7

 $x-5y\le-20$  

Example 8

 $5x+3y>6$  

Multiple Choice

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

•  $x+2y\le8$  

•  $x+2y\ge8$  

•  $x-2y\ge8$  

•  $x-2y\le8$  

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One line passes   $\left(2,8\right)$  and  $\left(-3,13\right)$  . A second line passes through the points    $\left(1,3\right)$  and  $\left(5,7\right)$ . At what point do the two lines intersect?

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Daniel and Natalie are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and strawberry cheesecakes. Daniel sold 7 New York style cheesecakes and 14 strawberry cheesecakes for a total of $210. Natalie sold 14 New York style cheesecakes and 11 strawberry cheesecakes for a total of $216. Find the cost each of one New York style cheesecake and one strawberry cheesecake.

(New York style cheesecake, strawberry cheesecake)

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Taylor’s aquarium has six times as many fish as frogs. If a quarter of her frogs plus a third of her fish equals nine, how many frogs does Taylor have in her tank?

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A boat traveled 189 miles downstream and back. The trip downstream took 9 hours. The trip back took 27 hours. Find the speed of the boat in still water and the speed of the current.

(boat, current)

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A fishing boat left Port 59 and traveled west. An aircraft carrier left two hours later traveling at 25 mph in an effort to catch up to the fishing boat. After traveling for three hours the aircraft carrier finally caught up. Find the fishing boat's average speed.

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

 $y=-7x+16$  
 $-7x-6y=9$  

Multiple Choice

The table below shows the population of a city x years since 1990. If the population continues to grow at a linear rate, what will be the approximate population in 2020?

• 41,400

• 45,700

• 51,300

• 56,800

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

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

 $-2\left|2x+2\right|-1=-5$  

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

 $-8x+6\left(1-4x\right)=4\left(7-8x\right)$  

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Two linear functions are shown. What is the distance between the x-intercepts of the two functions?

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

 $\frac{a^0b^3\times\left(a^{-4}\right)^0}{2ba^2}$  

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The table shows the height of a hot-air balloon, based on the number of minutes since it left the ground. What was the average height increase between 15 and 30 minutes?