Algebra 1--Three Word Problems (Reiny or Kuai)

Can anyone thoroughly explain how to solve these problems as well as how to graph them?

1. Linda works at a pharmacy for $15 an hour. She also baby-sits for $10 an hour. Linda needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. Show and describe the number of hours Linda could work at each job to meet her goals. List two possible solutions.

2. Theo's mother has given him at most $150 to buy clothes for school. The pants cost $30 each and shirts cost $15 each. How many of each can he buy? Write a linear inequality to describe the situations. Graph the linear inequality and give three possible combinations of pants and shirts Theo could buy.

3. A grocer sells mango for $4/lb and apples for $3/1b. The grocer starts with 45 lb of mangos and 50 lb of apples each day. The grocer's goal is to make at least $300 by selling mangos and apples each day. Show and describe all possible combinations of mangos and apples that could be sold to meet the goal. List two possible combinations.

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  1. to graph inequalities, draw the lines that represent the equations (as if not inequalities). Then shade the area above or below the line, depending on whether y is greater or less than the values on the line.

    For example, on #1, if Linda works p hours at the pharmacy and b hours babysitting,

    p+b <= 20
    15p+10b >= 90

    To see the solution, check out the shaded region here:

    http://www.wolframalpha.com/input/?i=plot+p%2Bb+%3C%3D+20+and+15p%2B10b+%3E%3D+90+and+p%3E%3D0+and+b%3E%3D0

    Do the others in like wise -- devise your inequalities and then discover the shaded region.

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    posted by Steve
  2. hours worked in pharmacy --- x
    hours worked baby-sitting ---- y

    15x + 10y ≥ 90 , or after simplifying
    3x + 2y ≥ 18

    also x+y ≤ 20

    sketching the region below y = -x + 20
    and the region above the line y = (-3/2)x + 9
    in the first quadrant yields many ordered pairs that satisfy both inequalities.
    e.g.
    10, 10
    11, 8
    11, 7

    try #2 and #3 using the same method I used for the first one.

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    posted by Reiny
  3. I still don't know how to graph #2.

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  4. I have absolutely no idea of how to solve #3, either.

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  5. #2.
    30p+15c <= 150

    #3.
    0 <= m <= 45
    0 <= a <= 50
    4m + 3a >= 300

    see the solution at

    http://www.wolframalpha.com/input/?i=solve+0+%3C%3D+m+%3C%3D+45%2C+0+%3C%3D+a+%3C%3D+50%2C+4m+%2B+3a+%3E%3D+300

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    posted by Steve

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