Write an Equation to solve a problem (show all working out)?

Question

A) I am a counting number. If you were to multiply me by 3 and add 6 the result would be 30. What number was I to start with ?

B) The sum of 2 consecutive numbers is 33 what are the numbers.

C) The lenght of a rectangle is 5cm longer then its width. If the perimenter of the rectangle is 50cm , What is the lenght ?

D The combined age of mike and tom is 39. If mike is twice as old as tom how old is mike?

E) The length of a rectangle is twice its width. If the perimeter of the rectangle is 36cm, what is the lenght ?

Answer 1

X=(30-6)/3

2X=33-1

Answer 2

A) 30 - 6 = 24
24/3 = 8
The original number is 8

B) 33 = 2X + 1
32 = 2X
x = 16
16 and 17 are the numbers

C) The perimeter is X + (X + 5) + X + (X + 5)
4X + 10 = 50
4X = 40
X = 10
10 + 5 = 15
The length is 15 cm.

D) 3X = 39
39 / 3 = 13
X = 13
13*2 = 26
Mike is 26

E) 36 = X + 2X + X + 2X
36 = 6X
x = 6
2X = 12
The length is 12 cm.

Answer 3

Problem 1)

Let x be the counting number. If you multiply it by 3 and add 6, you get 30:

3x + 6 = 30
3x = 24
x = 8

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Problem 2)

The sum of two consecutive numbers is 33.
Let x be the first number. Then x+1 is the second number:

x + x+1 = 33
2x + 1 = 33
2x = 32
x = 16

The first number is 16, so the second number is 17

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Problem 3)

You have a rectangle with width x. The length is 5 cm longer than the width, so the length is x+5. The perimeter of the rectangle is 50cm, which is found by the formula 2*(length + width):

2*[(x+5) + x] = 50
2*(2x + 5) = 50
4x + 10 = 50
4x = 40
x = 10

So, the width is 10cm. The length is 5cm longer, so the length is 15cm

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Problem 4)

Mike and Tom's ages added together equals 39. Let x by Tom's age. Mike is twice as old as Tom, so Mike's age is 2x:

x + 2x = 39
3x = 39
x = 13

Tom is 13, so if Mike is twice as old, Mike is 26.

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Problem 5)

Let x be the width of the rectangle. The length is twice the width, so the length is 2x. The perimeter is found by the formula 2*(length + width). The perimeter is 36cm:

2*(2x + x) = 36
2*(3x) = 36
6x = 36
x = 6

So, the width is 6cm. Since the length is twice the width, the length is 12cm.

Answer 4

Let's name the number we look for X

A) X*3 + 6 =30 so X*3=30-6 so X*3=24 so X=24/3

so X=8

B) X and consecutive is Y=X+1 so
X+Y=33 so X+X+1=33 so 2X=33-1 so 2X=32 so X=32/2 so X=16

so our numbers are 16 and 17

C) L=lengt W=width so we have L=W+5
The perimeter=L+L+W+W so we have
L+L+W+W=50 so replacing L with W+5
(W+5) + (W+5) +W+W=50
4W+10=50
4W=40
W=40/4
W=10 so the length is L=W+5=10+5=15

D) Mike's age=M
Tom's age=T
M+T=39
M=2*T
So 2*T+T=39
3T=39
T=13
So that means Mike is 2*13=26 years old

E) L=2*W - length of a rectangle is twice its width

L+L+W+W=36 -perimeter of the rectangle is 36cm

2*W+2*W+W+W=36
6W=36
W=36/6
W=6

So length is L=2*W=2*6=12

Answer 5

A) Let N be the original number.
Then 3N + 6 = 30
Subtract 6 from both sides
3N = 30 - 6 or 24
N = 24/3 or 8

B) Let N be the lower number
Then 2N + 1 = 33
Subtract 1 from both sides
2N = 33 - 1
N = 32/2 or 16
the numbers are 16 & 17

C) Let W be the width of the rectangle
The length will be W + 5 cm
The perimeter will be:
4W + 10 = 50
W = 40/4 or 10
The length will be 15

Answer 6

A. 30-6=24
24/3=8

B. 16+17=33

C. 2(w+5)+2w=50
2w+10+2w=50
4w+10=50
-10 -10
4w=40
4w/4 40/4 spacing is off, divide both sides by 4
w=10
10+5=15 cm is the length

D. m=2t
2t+t=
3t=39
3t/3 39/3 divide both sides by 3
t=13
Tom is 13 and mike is twice as old so mike is 13(2)=26 years.

E. L=2w
2L+2w=36
2(2w)+2w=36
4w+2w=36
6w=36
6w/6 36/6 divide both sides by 6
w=6
if L=2w, then L=2(6) which is 12 cm

hope that helps some! if u dont understand something, just tell me and i'll explain!

Answer 7

A. 3x+6=30; x = (30 - 6)/3 = 8
B. x + (x+1) = 33; 2x + 1 = 33; x = 16
C. 2w + 2(w+5) = 50; 4w = 40; w = 10cms
D. m + t = 39; 2t + t = 39; t = 13; m = 2 * 13 = mike = 26years
E. 2w + 2(2w) = 36 = 6w; w = 6; l = 12 = length;

Answer 8

A.... (30-6)/3

B.... X+(X+1)=33 solve for X

C... 2X+2(X+5) =50 X+5 is the length

D... X+2X=39 2X is the age of Mike

E... 2X + 2(2X)=36cm 2X is the length


This is as far as I will take you... if you can't do the algebra sorry :-)

Answer 9

a) 3x + 6 = 30
x = 8
b) x + x + 1 = 33
2x = 32
x = 16
c) m + t = 39
m = 2t
2t + t = 39
3t = 39
t = 13
d) L = 2W
2L + 2W = 36
2L + L = 36
3L = 36
L = 12

Answer 10

A) 3x+6=30
this gives: x=8
B) y+(y+1)=33
numbers are: y=16; y+1=17
C)2(L+(L-5))=50
length is, L=15 cm
D)2x+x=39
age of Mike=13
E)2(L+.5L)=36
length is, L=12 cm