Explore BrainMass

Explore BrainMass

    Equations

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    An invoice for 17 brooms and 22 mops totaled 211.84. Another invoice for 20 brooms and 14 mops totaled 191.00 How much did each broom cost, and how much did each mop cost (to the nearest cent)?

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf
    https://brainmass.com/math/algebra/determining-system-equations-solve-unknown-variables-15346

    SOLUTION This solution is FREE courtesy of BrainMass!

    Let the brooms cost be denoted by x and the mops cost be denoted by y

    invoice for 17 brooms and 22 mops totaled 211.84
    or 17 x + 22 y= 211.84 ---Equation1

    invoice for 20 brooms and 14 mops totaled 191.00
    or 20 x + 14 y= 191 ---Equation2

    Now we have two equations and and an equal number= two unknowns
    Thus the equations can be solved simultaneously to give the values of x and y

    17 x + 22 y= 211.84 ---Equation1
    20 x + 14 y= 191.00 ---Equation2

    Multiplying both the left and right hand sides of an equation does not change the equation

    We multiply equation 1 throughout by 20

    17 x + 22 y= 211.84 ---Equation1 x 20
    = 340 x + 440 y= 4236.80

    We multiply equation 2 throughout by 17

    20 x + 14 y= 191.00 ---Equation2 x 17
    = 340 x + 238 y= 3247.00

    Thus we get equations 1 and 2 as

    340 x + 440 y= 4236.8 ---Equation1
    340 x + 238 y= 3247.00 ---Equation2

    Next we subtract equation 2 from equation 1

    340 x + 440 y= 4236.8
    340 x + 238 y= 3247
    0 x + 202 y= 989.80

    0r 202 y= 989.80
    or y= 4.90 =989.8/202

    We can substitute the value of y= 4.90 in either of equation 1 or 2 to get the value of x

    Thus equation 1=
    17 x + 22 y= 211.84 ---Equation1
    Substituting the value of y= 4.90 in this equation
    17 x + 107.8 = 211.84
    or 17 x= 104.04 =211.84-107.8

    or x= 6.12 =104.04/17

    Thus the value of x= price of the broom= $6.12
    The value of y= price of the mop= $4.90

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf>
    https://brainmass.com/math/algebra/determining-system-equations-solve-unknown-variables-15346

    Attachments

    ADVERTISEMENT