Math 1 22 Feb

Math 1

February 22, 2021

Example 1

To build the garden of your dreams you need 8 m³ of soil containing 85% silt. You have two types of soil you can combine to achieve this: soil with 40% silt and pure silt. How much of each soil should you use?

Example 2

A metallurgist needs to make 15 oz. of an alloy containing 74% copper. She is going to melt and combine one metal that is 35% copper with pure copper. How much of each should she use?

Example 3

Fruit salad which costs $5/kg is made by combining sliced peaches which cost $8/kg with sliced bananas which cost $4/kg. Find the number of kg of sliced peaches and sliced bananas required to make 16 kg of fruit salad.

Example 4

Write down the coordinate pairs of the two points you see in this image. Move on to the next slide to watch the video example of how to solve this problem.

Example 5

Write down the coordinate pairs of the two points you see in this image. Move on to the next slide to watch the video example of how to solve this problem.

Example 6

Working alone, Nicole can mop a

warehouse in four hours. Ashley can mop the same warehouse in eight hours. Find how long it would take them if they worked together. Round to the nearest tenth.

Example 7

It takes Scott six minutes to sweep a

porch. Kim can sweep the same porch in five minutes. Find how long it would take them if they worked together. Round to the nearest tenth.

Multiple Choice

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

The function  $C\left(m\right)=0.55m+3.75$  models the cost to take an m mile-long taxi ride from Quick Cabs. The table below shows the cost to take a cab different distances from Get You There Cabs. Which statement is true about the two cab companies?

• Quick Cabs costs less per mile but has a higher fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile but has a lower fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile but has a higher fixed fee than Get You There Cabs.

• Quick Cabs costs less per mile but has a lower fixed fee than Get You There Cabs.

Fill in the Blanks

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

The cost of 10 gallons of regular paint and 15 gallons of delux paint is $315. If the delux paint costs $6 more per gallon than the regular paint, what is the cost for 20 gallons of regular paint?

Fill in the Blanks

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

Two trains, 165 miles apart, travel toward each other in a straight line from opposite directions. The commuter train is traveling due north at an average speed of 65 miles per hour. The express train is traveling due south at an average speed of 75 miles per hour. If both trains left at the same time, in how many minutes will the trains be 25 miles apart?

Multiple Choice

Quiz 16 Review Question: Go look up what you answered, keep it the same if it was correct.

Which is an equation of the line graphed below?

• $y=2.5x-2$

• $y=0.4x+5$

• $y=2.5x+5$

• $y=0.4x-2$

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Find the missing side length of the triangle. Round to the nearest tenth.

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Find the missing side length of the triangle. Round to the nearest tenth.

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An isosceles triangle has congruent sides of 20 cm. The base of the triangle is 10cm. What is the area of the triangle? Round to the nearest whole number.

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Anjali wants to make 17 qt. of a 48% sugar solution by mixing together a 4% sugar solution and a 72% sugar solution. How much of each solution must she use?

(4% solution, 27% solution)

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Generic sugar which costs $3/lb is made by combining brand X sugar which costs $5/lb with brand Y sugar which costs $1/lb. Find the number of lb of brand X sugar and brand Y sugar required to make 18 lb of generic sugar.

(brand X, brand Y)

Multiple Choice

The table shows per capita consumption of bottles water for selected years, 1980-2005. Based on a line of best fit of the data, about how fast is the consumption of bottled water growing each year?

• 0.59 gallon per capita per year

• 0.86 gallon per capita per year

• 0.91 gallon per capita per year

• 1.09 gallon per capita per year

Fill in the Blanks

4 L of an alcohol solution was mixed with 10 L of a 90% alcohol solution to make a 70% alcohol solution. Find the percent concentration of the first solution.

Multiple Choice

What is the system of inequalities displayed in the graph?

• $x-y\ge-8$
  $5x+y>2$
  

• $x-y\le-8$
  $5x+y>2$
  

• $x-y\le-8$
  $5x+y<2$
  

• $x-y\ge-8$
  $5x+y<2$
  

Multiple Choice

Which graph displays the following system of inequalities?

 $y>x+1$  
 $y<4x-2$  

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

 $\frac{2x^0y^4\times\left(2x^4y^{-2}\right)^2}{x^0y^0}$  

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The senior classes at High School A and High School B planned separate trips to the local amusement park. The senior class at High School A rented and filled 9 vans and 11 buses with 375 students. High School B rented and filled 3 vans and 3 buses with 111 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)