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Math Help - Word Problem Help

  1. #1
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    Word Problem Help

    Can someone show me how to do this question? Thanks.

    Ralph works part-time for a bike repair shop. He earns $2 for each tire he installs and $5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned $110. How many of each type of installation did he complete?
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  2. #2
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    Quote Originally Posted by andi01 View Post
    Can someone show me how to do this question? Thanks.

    Ralph works part-time for a bike repair shop. He earns $2 for each tire he installs and $5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned $110. How many of each type of installation did he complete?
    Hi andi01,

    State what you know and what you don't know:

    Let x = the number of tires installed

    Let 40 = total number of installations

    Let 40 - x = the number of gears he assembles

    Let 2x = earnings on tire assemblies

    Let 5(40 - x) = earnings on gear assemblies

    Let 110 = total earnings

    Use the last three statements to set up your equation.

    2x + 5(40 - x) = 110

    I think you might be able to take it from here.
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  3. #3
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    Also andi01, if you prefer, you could use two equations and solve a system of equations to get the same results.

    Let x = number of tire assemblies

    Let y = number of gear assemblies

    Let 40 = total assemblies

    (1) x + y = 40

    Let 2x = earnings on tire assemblies

    Let 5y = earnings on gear assemblies

    Let 110 = total earnings

    (2) 2x + 5y = 110

    Solve the system of equations (1) and (2).
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  4. #4
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    Quote Originally Posted by masters View Post
    Also andi01, if you prefer, you could use two equations and solve a system of equations to get the same results.

    Let x = number of tire assemblies

    Let y = number of gear assemblies

    Let 40 = total assemblies

    (1) x + y = 40

    Let 2x = earnings on tire assemblies

    Let 5y = earnings on gear assemblies

    Let 110 = total earnings

    (2) 2x + 5y = 110

    Solve the system of equations (1) and (2).
    How do you solve system of equations?
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  5. #5
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    Quote Originally Posted by andi01 View Post
    How do you solve system of equations?
    (1) x + y = 40

    (2) 2x + 5y = 110
    -----------------------

    Multiply equation (1) by -5 to get equation (3) and then add to (2). This will eliminate the y variable.

    (3) -5x - 5y = -200

    (2) 2x + 5y = 110
    -----------------------

    -3x = -90

    x = 30

    Substitute this value into (1) to find y.

    (1) x + y = 40

    30 + y = 40

    y = 10
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  6. #6
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    Quote Originally Posted by andi01 View Post
    Can someone show me how to do this question? Thanks.

    Ralph works part-time for a bike repair shop. He earns $2 for each tire he installs and $5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned $110. How many of each type of installation did he complete?
    <br />
2x + 5y = 110.........\left( 1 \right)<br />
    <br />
x + y = 40.............\left( 2 \right)<br />

    <br />
\text{Multiplying }\left( \text{2} \right)\text{ by  - 2 and adding to }\left( \text{1} \right)<br />

    <br />
\text{and with a bit of algebra manipulation}<br />

    <br />
\text{you get: }<br />

    <br />
y = 10\text{ and }x = 30<br />

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