Can someone help me with this pleaseeeee (In details plzzzzzzzzz)?

Question

1)Find two consecutive even integers such that twice the smaller is 26 less than3 times the smaller.

2) Find three consecutive even integers such that the sum of the smallest and twice the second is 20 more than the thrid.

Answer 1

It's not in your textbook?

Answer 2

1)
Find two consecutive even integers such that twice the smaller is 26 less than3 times the smaller.

I think you mean, "Find two consecutive even integers such that twice the smaller is 26 less than3 times the larger."

Use these equations to turn the word problem into a math problem:
a. I1 = I2 + 2, where I1 = smaller, I2 = larger
and therefore I2 = I1 - 2
b. 2*I1 = 3*I2 -26 [from problem statement]
then substitute I2 in a) in equation b):
2*I1 = 3*(I1-2) - 26
or,
2I1 = 3I1 - 6 - 26
I1 = 20
then, I2 = 22 from equation a)
---------
2)
"Find three consecutive even integers such that the sum of the smallest and twice the second is 20 more than the third."

Convert the word problem to a math problem:
I1 + 2*I2 = I3 + 20

Also we know that:
I3 = I2 + 2
and
I2 = I1 + 2
See if you can solve this one by substitution like I did in the first problem.

Hope this helps!

Answer 3

1) n = smaller number

2n + 26 = 3n
-2n -2n
n=26

Since the numbers are consecutive EVEN numbers, add 2 to n to get 28. Therefore the ANSWERS are 26 and 28.


2) n = smallest number
n + 2 = middle number
n + 4 = largest number

n + 2(n + 2) - 20 = n + 4
n + 2n + 4 - 20 = n + 4
-n -4 -n -4
2n - 20 = 0
+20 +20
2n = 20
n=10

Since the numbers are consecutive EVEN integers, add 2 and then 2 more to n, creating the ANSWERS 10, 12, and 14.

Answer 4

1) 20 and 22; b/c (3*22)-26= (2*20)

2) 10, 12, 14