70.9k views
3 votes
Solve.One number is 4 less than a second number. Twice the second number is 30 more than 4 times the first. Find the two numbers.

Solve.One number is 4 less than a second number. Twice the second number is 30 more-example-1
User Narkeeso
by
8.2k points

1 Answer

2 votes

From the information available;

Let the numbers be x and y.

One number is 4 less than a second number. This would be tranlated as x is 4 less than y, or;


x=y-4

Also, twice the second number is 30 more than 4 times the first, that is


\begin{gathered} 2* y=30+(4* x) \\ OR \\ 2y=30+4x \end{gathered}

We now have a system of simultaneous equations which we shall solve as follows;


\begin{gathered} x=y-4---(1) \\ 2y=30+4x---(2) \\ \text{Substitute for x=y-4 into equation (2)} \\ 2y=30+4(y-4) \\ 2y=30+4y-16 \\ \text{Collect all like terms;} \\ 2y-4y=30-16 \\ -2y=14 \\ \text{Divide both sides by -2;} \\ -(2y)/(-2)=(14)/(-2) \\ y=-7 \\ \text{Substitute for the value of y into equation (1)} \\ x=y-4 \\ x=-7-4 \\ x=-11 \end{gathered}

ANSWER:

The two numbers are;


-11\text{ and -7}

User Danny Whitt
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories