two word problems?

Question

1. After watching hours of those home improvement shows, you decide you want to paint you bedroom. You don’t want to paint all four walls the same color (how boring!), but instead, you want to paint one wall a different color. The electric orange paint you’ve chosen for the "special" wall is more expensive, and you’re on a budget, so you need to know the area of the wall so you can buy the smallest amount of paint possible. You know that the height of the wall is half the length. You also know that the perimeter of the rectangular wall is 48 feet. What is the area of the wall?


A The area of the wall is 116 sq. ft.
B The area of the wall is 128 sq.ft.
C The area of the wall is 144 sq. ft.
D The area of the wall is 140 sq. ft.
E The area of the wall is 416 sq. ft.
F The area of the wall is 136 sq. ft.

for this 1 its like the addition method or something
2.
3x + 5y = -11

6x – 5y = -16

A (3, 1/6)
B (-3, -4)
C (2, -1)
D (-3, -2/5)
E (-2, 4/5)
F (3, -4)

Answer 1

l=2h
2l + 2h = perimeter=48
2l+ l =48
3l = 48
l=16ft
h=8 ft
area = 128 sq ft the answer is b


3x + 5y = -11
6x-5y =-16
9x =-27 (added the two equations)
x=-3
-9 +5y =-11
5y =-2
y = -2/5
the answer is D

Answer 2

okay, for 1)
a)you know that the height of the wall is half of the length, therefore you can denote the height of the wall as x and the length of the wall as 2x (twice the length of the height).
b) the equation for finding the perimeter of a rectangle is P=2l+2w where P=perimeter, l=length, w=width
c) so we substitute in the values from "a" and we know that P=48; l=2x, w=x: so we get 48=2(2x)+2(x) which gives us a value of x=8 which means w=8.
d) because w=x=8, that means l=2x=16
e) the equation for area of a rectangle is Area=l x w
f) so we substitute in Area=16 x 8 and get a value of 128sq ft<--- don't forget units
which is choice B

*the final answer is B
---
2)
this is an addition method. let's say equation 1 is 3x + 5y= -11 and equation 2 is 6x - 5y= -16
a) if you look closely, in equation 1 we have +5y and in equation 2 we have -5y, that means if we add them we will be able to cancel them out and just solve for x
b) so equation 1 + equation 2 gives us 9x= -27, which gives x= -3
c) we now have x! we can take x and plug it back into either equation 1 or equation 2. so let's plug it into both just to see what we get!
d) equation 1: 3(-3) + 5y= -11 --->5y= -2 ---> y= -2/5
equation 2: 6(-3) -5y= -16 ---> -5y=2--->y= -2/5
good! we get the same value for y
e) so we have x= -3 and y= -2/5
f) the form that the answer is given is in coordinate form where (x,y) so substituting in our values gives us (-3,-2/5) which is the same as "D"

*the final answer is D

i hope that helped. the key to solving word problems is to look for clues, it's kind of like a puzzle/hunt for the pieces. with practice problems like this will become a piece of cake! best of luck in your future math endeavors!! :-)

Answer 3

1) the answer is B

The height of the wall (h) is x, therefore the length is 2x.
perimeter:
2x+x+2x+x=48
6x=48
x=8
area:
area= l*w
=(2x)*x
=(2*8)*8
=128

2) Solve one equation for x or y and insert into other equation:
3x+5y=-11
3x=-11-5y
x=-11/3 - 5/3y

6(-11/3 - 5/3y) - 5y = -16
-66/3 - 30/3 y - 5y =-16
-22-10y-5y=-16
-15y=6
y=-6/15= -2/5

x=-11/3 - 5/3y
x=-11/3 - 5/3(-6/15)
x=-11/3+30/45
x= -11/3 + 2/3
x= -9/3 = -3

The answer is D

Answer 4

The height (h) is (equals) half the length (½L)
h = ½L.
The perimeter (2h + 2L) is (equals) 48 feet.
2h + 2L = 48. Substituting,
2(½L) + 2L = 48,
L + 2L = 48,
3L = 48,
L = 16 feet. The height is ½(16) = 8 feet.
The area is Lh = (16 ft)(8 ft) = 128 sq. ft.

3x + 5y = -11
6x - 5y = -16. Adding both lines eliminates the y term.

9x = -27,
x = -3. Substitute to find y:

3x + 5y = -11,
3(-3) + 5y = -11,
-9 + 5y = -11. Adding 9,
5y = -2. Dividing by 5,
y = -2/5.

The solution is (-3, -2/5).

Answer 5

1)
P = 48 = 2L + 2W = 2L + 2(1/2)L
48 = 3L
L = 16, W = 8, so
A = 16(8) = 128 ft²

2)
add the equations and get
9x = -27
x = -3
3(-3) + 5y = -11
5y = -2
y = -2/5
answer D (-3, -2/5)

Answer 6

1. B
2. D