Equations

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

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