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Question

The first problem

Find two consectutive integers such that the sum of 4 times the first integer and 2 times second integer is 62.

The second problem

The difference of two numbers is 14. The second is 1 less then 2 times the first. What are the two numbers.

I am completely confused What do I do??

Answer 1

First problem)
Two consecutive integers are i and (i+1).
4i + 2(i+1) = 62
4i + 2i + 2 = 62
6i = 60
i=10

The consecutive integers are 10 and 11.

Second Problem)
x-y=14
y=2x-1

Substitution.
x-(2x-1)=14
x-2x+1=14
-x=13
x=-13
y=-27

(-13) - (-27) = (-13) + 27 = 14.
2 x (-13) - 1 = (-26) - 1 = (-27) = y

Answer 2

First problem:

let x - first integer therefore (x + 1) is the second integer
equation then is: 4x + 2 (x +1) = 62
4x + 2x + 2 = 62
6x = 60
x = 10 (first integer)
x + 1 = 11 (next integer)

second problem: let x - second number and y = first number
2 equations would be: x - y = 14
x - 2y = -1
subtrating the two equations would result to: y = 15
x = 29

Answer 3

Lets work through this so you understand the logic.

You know the following
4X + 2Y = 62 the sum of 4 times the first integer and 2 times second integer is 62

X + 1 = Y (the numbers are consecutive)

Substitute for Y
4X + 2(X + 1) = 62
4X + 2X + 2 = 62
6X = 60
X = 10
Y = 11
Proof
4(10) + 2(11) = 62
40 + 22 = 62
62 = 62 (proved)
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Sorry but I am out of time... will check in later if it still is unanswered.

Answer 4

Problem 1: 4x+2y=62; y = x+1 (since the two integers are consecutive) => 4x+2(x+1)=62, solve for x

Problem 2: x-y=14, y = 2x-1. Substitute and solve.

Good luck

Answer 5

Okay, so write out an equation for the first one: 4x + 2 (x+1) = 62;
Now simplify the equation: 4x + 2x + 2=62, --> 6x + 2=62
Subtract 2 from both sides, so you are left with 6x=60;
And now divide both sides by 6 to get the x on its own: 6x/6=60/6;
Now you have your answer: x=10

Second question:
So: (x) - (2x - 1) = 14;
Simplify it: -x + 1 = 14;
Subtract 1 from each side to get the x on its own:
-x + 1 - (1) = 14 - (1) --> -x = 13
Multiply both sides by -1 so that x is positive: -x(-1) = 13(-1)
And your answer is: x = -13

If this made no sense to you at all, then feel free to say so and I'll explain it to you.

Answer 6

the first solution
let the two numbers be 'a' and 'a+!' as they are consecutive integers.
from the info
4a+2(a+1)=62
4a+2a+2=62
6a+2=62
6a=60
a=10

the second solution

if the two numbers are 'a' and 'b' then
b=one less than twice the first, ie 2a-1

lets write 2a-1 in the place of b
the difference of the two numbers
is a-b or
a-(2a-1)
a-2a+1 and this is 14
so -a+1=14
=> a= -13
the other number is 2(-13)-1= -27
=> b=-27

if ur confused wot to do, try yahoo ans's i think its worth the try ha

Answer 7

for me its just a guess and check useally i start out with whatever the end result is and find out what two numbers go into that number and work from there.

Answer 8

You are confused? Invest in algebrtor or you may be able to download it for free somewhere *thats what i did* it will walk you step by step.