One number is 2 more than 3 times another. Their

Emeli Hagan 2021-08-11 Answered
One number is 2 more than 3 times another. Their sum is 22. Find the numbers.
8, 14
5, 17
2, 20
4, 18
10, 12

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Jozlyn
Answered 2021-08-12 Author has 13445 answers

Let x represent the first number and y represent the second number.
The second number is 2 more than 3 times the first number:
\(\displaystyle{y}={2}+{3}{x}\)
The sum of the two numbers is 22:
\(\displaystyle{x}+{y}={22}\)
Let us replace y by \(2+3x\) in the previous equation (as \(y=2+3x\) holds):
\(\displaystyle{x}+{\left({2}+{3}{x}\right)}={22}\)
Combine like terms:
\(\displaystyle{2}+{4}{x}={22}\)
Subtract 2 from each side:
\(\displaystyle{4}{x}={20}\)
Divide each side by 4:
\(\displaystyle{x}={5}\)
Thus we obtain that the first number is x=5
Let us then determmine the second number by evaluating \(\displaystyle{y}={2}+{3}{x}\) as \(\displaystyle{x}={5}\):
\(\displaystyle{y}={2}+{3}{x}={2}+{3}{\left({5}\right)}={2}+{15}={17}\)
Thus the two numbers are then 5 and 17.
Result: 5 and 17

Have a similar question?
Ask An Expert
47
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-28
One number is 2 more than 3 times another. Their sum is 22. Find the numbers.
8, 14
5, 17
2, 20
4, 18
10, 12
asked 2021-08-03
To find: the unknown integer.
Given information: The GCF of 84 and another integer is 42, and their LCM is 252.
asked 2021-10-28
How many bit strings of length 10 have more 0s than 1s?
asked 2021-08-08
Discuss: Different Coordinate Systems As was noted in the overview of the chapter, certain curves are more naturally described in one coordinate system than in another. In each of the following situations, which coordinate system would be appropriate: rectangular or polar? Give reasons to support your answer.
a) You need to give directions to your house to a taxi driver.
b) You need to give directions to your house to a homing pigeon.
asked 2021-08-01
If repetitions are not permitted (a) how many 3 digit number can be formed from the six digits 2,3,5,6,7 and 9? (b) how many of these are less than 400? (c) how many are even? (d) how many are odd? (e) how many are multiples of 5?
asked 2021-07-31
\(\displaystyle{U}=\) the set of natural numbers between 10 and 20
\(\displaystyle{A}=\) Even Numbers
\(\displaystyle{B}=\) Multiples of 3 where the number is less than 18.
\(\displaystyle{C}=\) Composite numbers
Find \(\displaystyle{n}{\left({\left({A}{U}{B}\right)}\cap{C}\right)}\)
asked 2021-07-30
\(\displaystyle{U}=\) the set of natural numbers between 10 and 20
\(\displaystyle{A}=\) Even numbers
\(\displaystyle{B}=\) Multiples of 3 where the number is less than 18.
\(\displaystyle{C}=\) composite numbers
Find \(\displaystyle{\left({A}'{U}{C}\right)}-{B}\)
...