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?

MrPatel
Feb 22, 2018

#1**+3 **

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

hectictar
Feb 22, 2018

#2**+3 **

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.

hectictar
Feb 23, 2018

#3**+3 **

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)

ElectricPavlov
Feb 23, 2018