32.4k views
0 votes
The sum of two numbers is 7. Find the numbers

The sum of two numbers is 7. Find the numbers-example-1
User Chazu
by
7.8k points

1 Answer

4 votes

Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.

Solution:

Let x be the larger number and y be the smaller number such that;


\begin{gathered} x+y=7\ldots.\ldots\ldots\text{equation}1 \\ 5x+4y=48\ldots\ldots\text{.equation}2 \end{gathered}

From equation 1, we have;


\begin{gathered} x+y=7 \\ x=7-y\ldots\ldots\ldots....\text{equation}3 \end{gathered}

Substitute equation3 in equation2, we have;


\begin{gathered} 5x+4y=48 \\ 5(7-y)+4y=48 \\ 35-5y+4y=48 \\ -1y=48-35 \\ -1y=13 \\ \text{Divide both sides by -1;} \\ -(1y)/(-1)=(13)/(-1) \\ y=-13 \end{gathered}

Then, substitute the value of y in equation3;


\begin{gathered} x=7-y \\ x=7-(-13) \\ x=7+13 \\ x=20 \end{gathered}

Thus, the larger number is 20 and the smaller number is -13

User FreeVice
by
8.3k 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