The larger of two numbers is 1 more than twice the smaller. The sum of the numbers is 20 less than three times the larger. Find the numbers.

Question

05-11-2026
Mathematics

Answered

The larger of two numbers is 1 more than twice the smaller. The sum of the numbers is 20 less than three times the larger. Find the numbers.

Verified Answer :

Related Questions

Economic growth can result from an in government expenditures and an in net exports a increase increase b decrease decrease c increase decrease I know its not C

What is the plural of cameo cameos cameoes both

Moussa delivered 38 of the newspapers on his route in the first hour and 45 of the rest in the second hour What fraction did he deliver in the second hour

A set of equations is given below Equation C y 6x 9 Equation D y 6x 2 Which of the following options is true about the solution to the given set of equations On

SAT Question of the Day The scientist ascribed the of the parks remaining trees to the of the same termite species that had damaged homes throughout the city A

name two ways that communities can reduce their collective ecological footprint

Why was Wilhelm II determined to build up the German army and navyPoints 3

Identify the scenario that demonstrates the process of cultural diffusion a farmer growing crops on a cultivated plot of land the spread of illness from animalb

Which of the following best describes a disadvantage of a representative democracy compared to a direct democracy Elections are unnecessary because birth and po

Help with Frations please Gigi puts cup of white flour and cup of wheat flour into her bread recipe How many cups of flour does Gigi use in all

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T23:50:13-05:00

Define the larger number \(x\) and the smaller number \(y\).
Translate the given conditions into two equations: \(x = 2y + 1\) and \(x + y = 3x - 20\).
Substitute the first equation into the second to solve for \(y\), yielding \(y = 6\).
Use \(y = 6\) to find the larger number \(x = 13\).
The final numbers are 13 and 6. \(\boxed{13, 6}\).

Explanation

Analysis of the Problem and Variables

We are looking for two numbers, a larger one and a smaller one. Let \(x\) represent the larger number and \(y\) represent the smaller number. We are given two conditions based on the problem statement:

The larger number is 1 more than twice the smaller: \(x = 2y + 1\).
The sum of the numbers is 20 less than three times the larger: \(x + y = 3x - 20\).

These two equations form a system of equations that we can solve for \(x\) and \(y\).

Solving for the Smaller Number y

To find the values, we can substitute the expression for \(x\) from the first equation into the second equation:
\((2y + 1) + y = 3(2y + 1) - 20\).
First, simplify the left side:
\((2y + 1) + y = 3y + 1\).
Next, simplify the right side by distributing the 3:
\(3(2y + 1) - 20 = 6y + 3 - 20 = 6y - 17\).
Now, set the simplified sides equal to each other:
\(3y + 1 = 6y - 17\).

Finding the Larger Number x and Conclusion

Now we solve the equation \(3y + 1 = 6y - 17\) for \(y\). Subtract \(3y\) from both sides:
\(1 = 3y - 17\).
Add 17 to both sides:
\(18 = 3y\).
Dividing by 3 gives:
\(y = 6\).
Now that we have the value of the smaller number, we can find the larger number \(x\) using the first equation, \(x = 2y + 1\):
\(x = 2(6) + 1 = 12 + 1 = 13\).
The larger number is 13 and the smaller number is 6.

Examples

This problem can be applied in real-world scenarios where you have constraints on multiple resources or quantities. For instance, imagine managing inventory for two types of products. If the amount of product A is related to the amount of product B by a specific formula, and their total sum must meet a target derived from the amount of one of them, setting up a system of linear equations is the perfect way to determine the exact quantities needed. This ensures that all operational requirements are met precisely and efficiently.