+166 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?
+9481 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
+9481 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.
+37153 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)
