Did you know?
Did you know that algebra can help us solve word problems? In this problem, we are given two numbers, with one being 18 more than 5 times the other. We can represent the smaller number as "x" and the larger number as "5x + 18".
We are also told that if we multiply the larger number by 3 and add 4 times the smaller number, the result is 16. So we can set up an equation:
3(5x + 18) + 4x = 16
To solve this equation, we first distribute the 3 to the terms inside the parentheses:
15x + 54 + 4x = 16
Then, we combine like terms:
19x + 54 = 16
Next, we subtract 54 from both sides of the equation:
19x = -38
Finally, we divide both sides by 19 to solve for x:
x = -2
By substituting this value back into our expression for the larger number, we find that the larger number is 5(-2) + 18 = 8.
So, the two numbers we found are -2 and 8. Algebra can be a powerful tool in solving problems like this!
