Word Problems

[sw87]

I am having trouble understanding the problem and setting up the equation.
Q:
The sum of two integers is eleven. One less than twice the larger number is five times the smaller number. What is the larger number?

I know they want to larger number.
I don't understand the 2nd sent. :roll:

I keep coming up with

11= (two integers)
L=large number S=small number
2L-1=5S

 

[soroban]

Hello, sw87!

Evidently, you don't understand the first sentence.

The sum of two integers is eleven.
One less than twice the larger number is five times the smaller number.
What is the larger number?

I know they want to larger number.
I don't understand the 2nd sentence.

I keep coming up with:

11 = (two integers) . How do you write this "in Algebra"?

L = large number, S = small number

2L - 1 = 5S

\(\displaystyle \text{We have: }\;\begin{array}{c}L + S \:=\;11 \\ 2L - 1 \:=\:5S\end{array}\)


\(\displaystyle \text{Solve the system: }\:\begin{Bmatrix}L + S &=& 11 \\ 2L - 5S &=& 1 \end{Bmatrix}\)

 

[sw87]

Thank you i think i figured it out to be the large number equals 8