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Solving Equations With 2 Variables

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On a jury, there are 3 fewer men than twice the number of women. If there were 2 more women on the jury, the numbers of men and women would be equal. How many men are on the jury?

Janet and Lynn live 8 mi apart in opposite directions from their office. If Lynn lives 1 mi less than twice as far from the office as Janet does, how far does each live from the office?

Feb 22, 2018

#1
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Let  m = the number of men

Let  w = the number of women

There are 3 fewer men than twice the number of women.

m  =  2w - 3

If there were 2 more women on the jury, the numbers of men and women would be equal.

w + 2  =  m       Subtract  2  from both sides of this equation to solve for  w .

w  =  m - 2        Now we can use this value of  w  in the first equation.

m  =  2w - 3

m  =  2(m - 2) - 3

m  =  2m - 4 - 3

m  =  2m - 7

m - 2m  =  -7

-m  =  -7

m  =  7  =  the number of men

Feb 22, 2018
#2
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Let  J  be the number of miles between Janet and the office.

Let  L  be the number of miles between Lynn and the office.

Janet and Lynn live 8 mi apart in opposite directions from their office.

J + L  =  8

Lynn lives 1 mi less than twice as far from the office as Janet does.

L  =  2J - 1    Use this value for  L  in the first equation.

J + (2J - 1)  =  8

3J - 1  =  8

3J  =  9

J  =  3     Use this value for  J  to find  L .

L  =  2J - 1

L  =  2(3) - 1

L  =  5

Janet lives  3  miles from the office, and Lynn lives  5  miles from the office.

Feb 23, 2018
#3
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y = men

x= women     (see what I did there?  Haha)

2x-3 = y

and  x+2 =y        so    2x-3=x + 2   (assuming there can be more than12 jurors)

x = 5 women    y = 7 men     12 jurors total

(if you add two women, the number of men and women will be equal, but 14 jurors total)

Feb 23, 2018
edited by ElectricPavlov  Feb 23, 2018