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# A few story-like math assignments I need help with x

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I really appreciate all the work the people on this site put in this, seriously, all of you are heroes and I can't thank you enough for how much you helped me. Thanks in advance once again if you can help me because I absolutely suck at linear equations and especially graphs <3 Also I'm not English so my grammar might be a tad off I apologize for that

1a. A family wants to buy carpet for their stairs and they ask two companies for the price. p is in the following formulas the price and t is the amount of stairsteps.

Company 1 uses p=25t

Company 2 uses p=140+15t

The stairs of the family consists of 14 stairsteps. Which of the two companies would be the cheapest option?

1b. Their neighbours also want to carpet their stairs. They have a few more stairsteps than the other family. Which option would be cheaper?

2a. There are two equatations: b=4a+8  and  b=-2a+30

What would be the graphs of both equations in the same coordinate system. Use for a the values 0 to 10.

2b. How do you solve the inequality of -2a+30>12 ? And how do you find this answer in the graph?

2c. What would be the coordinates of the break-even point? (Keep the fractions in the answer please so I can understand it better :"))

2d. For which value of a would the formula b=4a+8 give higher results than b=-2a+30 ?

3. Calculate the points of intersection of the following two pairs of equations.

y=5x+6 en y=9x-32

y=-0,5x+1,5 en y=-4(x-3)

Dec 12, 2017
edited by HeyxJacq  Dec 12, 2017

#1
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1 (a) Note that if we set the equations equal we have

25t  = 140  +  15t          subtract 15t from both sides

10t  = 140     divide both sides by 10

t = 14   equalizes the cost

So....for the first family, either option is the same

But...since the slope of  the first function - 25 - is greater than the other function - 15 ...this option will be more expensive after 14 steps.....so for the second  family, the second option is better than the first   Dec 12, 2017
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2....For this one....I'm using  x for a  and y for b

So we have

y  = 4x + 8

y = -2x +30

Here's the graph :  https://www.desmos.com/calculator/25etgvd1ja

2b

-2x + 30 > 12  subtract 30 from both sides

-2x  >  -18      divide both sides by  -2 and reverse the inequality sign

x <  9

Here's the graphical solution  : https://www.desmos.com/calculator/wqeiyuxd89

2c.....break even point.....set the functions equal  and solve for x

4x  + 8  =  -2x  + 30     add 2x to both sides, subtract 8 from both sides

6x  =  22     divide both sides by 6

x  = 22/6  =  11/3

And y  = 4(11/3)  +  8

y = 44/3  + 24/3

y = 68/3

Here's the graph with the break-even point  : https://www.desmos.com/calculator/iwcgpjjzqf

2d......we want to solve this

4x + 8  >  -2x  + 30

6x >  22

x > 22/6

x > 11/3   Dec 12, 2017
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Thank you CPhill! :")

Dec 13, 2017