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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)?

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!