Lisa is thinking about two positive integers. The larger integer is seven less than twice the smaller integer. The larger integer is also three more than the smaller integer.
What is the larger of the two integers that Lisa is thinking about?
~So the problem just throws me off completely cause there is no starting number.Please show me how to do it. Thanks!
let the numbers be L and S
L=2S-7
L=S+3
subtract the second equation from the first..
0=S-10
S=10 which makes L 13
No worries! Let's break down the problem step by step to figure out the larger integer that Lisa is thinking about.
Step 1: Assign variables
Let's assign variables to represent the two positive integers that Lisa is thinking about. We'll use "x" for the smaller integer and "y" for the larger integer.
Step 2: Set up equations
Based on the given information, we can set up two equations:
Equation 1: The larger integer is seven less than twice the smaller integer.
y = 2x - 7
Equation 2: The larger integer is three more than the smaller integer.
y = x + 3
Step 3: Solve the equations
Since both equations represent the same value for "y," we can equate them:
2x - 7 = x + 3
Simplifying this equation, we get:
2x - x = 3 + 7
x = 10
Step 4: Find the larger integer
Now that we have the value of x (the smaller integer), we can substitute it back into either equation to find the value of y (the larger integer).
Using Equation 2:
y = x + 3
y = 10 + 3
y = 13
So, the larger integer that Lisa is thinking about is 13.