Hi, all. I'm currently studying for a math test, and I was wondering if someone could help me solve these?

Question

The notes that I have aren't helping me much.

First problem:
A 9-foot board is cut into two pieces so that one piece is 5 feet longer than three times the shorter piece. Find the length of both pieces.

Second problem:
The number of women attending a math class was 9 less than twice the number of men. If a total of 63 students attended the class, how many were women?

I do remember doing these problems back in high school, but for some reason these are the only math problems I have trouble with! Any help is GREATLY appreciated. Thanks!

I have my answer! Thank you so much to everyone who responded!

Answer 1

PROBLEM 1:

Pick a variable x to represent the shorter piece. The longer piece is 5 feet longer than 3 times the shorter... in other words 3x + 5.

If you add these together you get 9 feet
x + 3x + 5 = 9
4x + 5 = 9
4x = 4
x = 1

So the shorter board is 1 ft. and the longer board is 8 feet.

PROBLEM 2:

Let m be the number of men
The number of women is 2m - 9

Added together you have 63 students:

m + 2m - 9 = 63
3m - 9 = 63
3m = 72
m = 24

So the class has 24 men and 39 women

Answer 2

Use equations: short piece = x and longer piece is 3x + 5 the total must be 9. So: x + 3x+5 = 9
4x = 9 - 5
4x = 4
x = 1
Short piece: 1 ft
Longer piece: 3(1) + 5 = 8 ft

Problem 2

Number of men: x Number of women: 2x - 9
Total: x + 2x - 9 = 63
3x = 63 + 9
3x = 72
x = 24
Number of men: 24
Number of women: 2(24) - 9
48 - 9
39

Answer 3

First problem: A 9-foot board is cut into two pieces so that one piece is 5 feet longer than three times the shorter piece. Find the length of both pieces.

x = length of the shorter board
y = length of longer board
y = 5 + 3x
Both boards together = 9

9 = x + (5 + 3x)
9 = 4x + 5 SUBTRACT 5 from both sides
4 = 4x DIVIDE both sides by 4
4/4 = x
1 = x LENGTH of shorter board

y = 5 + 3x
y = 5 + 3(1)
y = 8 LENGTH of longer board

ANSWER the boards are 1 foot and 8 feet long
---------------------------------------------------------
Second problem: The number of women attending a math class was 9 less than twice the number of men. If a total of 63 students attended the class, how many were women?

w = # of women
m = # of men
w = 2m - 9

63 = m + w
SUBSTITUTE the equation above for the # of women
63 = m + (2m - 9)
63 = 3m - 9 ADD 9 to both sides
72 = 3m DIVIDE both sides by 3
24 = m

w = 2m - 9
w = 2(24) - 9
w = 48 - 9
w = 39

ANSWER there are 39 women and 24 men in the class

CHECK
63 = m + w
63 = 24 + 39
63 = 63 it checks out

Answer 4

To solve these problems it is helpful to lable all the unknowns with variables:

1) 9-foot board is cut into 2 pieces... So lable the first piece as x and the second as y. Observe that x + y = 9, because the total length of pieces is equal to the length of the board. Hence y = 9 - x. Now the relationship between y and x can be expressed as y = 3x+5 (Why?) Substituting 9-x insread of y we obtain the following equation

9-x=3x+5.

2) Let w be the number of women attending the class and m be the number of men. Observe that w+m=63 (assuming that all students were either men or women of course). Hence w=63-m.

Observe that w=2m-9 or 63-m=2m-9.

Hope this helps

Answer 5

First problem:
x = length of the shorter piece, 3x + 5 = longer piece

Length of the shorter piece:
x + 3x + 5 = 9
4x = 4
x = 1

Length of the longer piece:
= 3(1) + 5
= 3 + 5
= 8

Answer: the shorter piece is 1 ft; the longer piece is 8.

Second problem:
x = no. of men, 2x - 9 = no. of women

No. of men:
x + 2x - 9 = 63
3x = 72
x = 24

No. of women:
= 2(24) - 9
= 48 - 9
= 39

Answer: 24 are men, 39 are women

Proof:
= 24 + 39
= 63

Answer 6

First problem:

The length of the short piece = x
The length of the longer piece = 3X + 5

Both of them put together is 9 ft

x + 3x + 5 = 9
4x = 9 - 5 = 4
x = 1 - This is the length of the short peice

The length of the longer peice = 9-1 = 8

Second problem:
Number of women = x
Number of men = 2x - 9

Total is 63

x + 2x - 9 = 63
3x = 72
x = 24 - This is the number of women
Number of men = 63 - 24 = 39

Answer 7

not to be rude to the first guy but actually the answer is that one board is 1ft long and the other is 8 ft long.
(1x3) + 5 = 8
i can't really give you a formula to figure that out or anything i just kindof played around with the numbers


and for the second question:
x = men
2x - 9 = women
*i used the words in the problem to derive this equation
total:
(2x - 9) + x = 63
3x - 9 = 63
3x = 72
x = 24
*remember x = men, so to find women plug in x to the equation for women:
2(24) - 9 = 39
there are 39 women in the class
check: 39 + 24 = 63

Answer 8

A. Let x= the shorter length
9=(3x+5)+x where 3x+5 = the longer piece
9=4x+5
4=4x
x=1 therefore the longer piece =8
B. let x=number of women
63= x+(2x-9) where 2x-9 = number of men
63=3x-9
63+9=3x-9+9
72=3x
x=24, men=2x+9=39

Answer 9

you opt for to get t by using itself so which you will use effortless math operations to achieve this. First you should multiply the two aspects by using 7 which will yeild: 4t - 3 = 14 (so we've been given rid of the fraction) Now upload 3 to the two aspects to yield: 4t = 17 (so we've been given rid of the -3) Now divide the two aspects by using 4 to get your answer: t = 17/4

Answer 10

1.
y = 3x + 5 <---- Length of one piece
y = 9 -x

3x+5 = 9-x
4x = 4
x = 1

2
W=2M -9
W =-M+63

2M-9 = -M +63
3M = 72
M = 24
W = 63 -24 = 39