Jon adds the expressions 5p + 2 and 2p + 1. Carlos adds the expressions 4p + 3 and 7p + 2.
To find the sum of the expressions, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the variable is "p" and it is raised to the power of 1.
Let's start with Jon's expressions: 5p + 2 and 2p + 1.
To add these expressions, we add the coefficients (numbers in front of the variable) of the like terms. So, the coefficient of "p" in the first expression is 5, and the coefficient of "p" in the second expression is 2.
Adding the coefficients, we get 5 + 2 = 7.
Now, let's add the constant terms (numbers without a variable). The constant term in the first expression is 2, and the constant term in the second expression is 1.
Adding the constants, we get 2 + 1 = 3.
Combining the coefficients and constant terms, the sum of Jon's expressions is 7p + 3.
Now, let's move on to Carlos's expressions: 4p + 3 and 7p + 2.
Following the same process, we add the coefficients of the like terms. The coefficient of "p" in the first expression is 4, and the coefficient of "p" in the second expression is 7.
Adding the coefficients, we get 4 + 7 = 11.
Next, we add the constant terms. The constant term in the first expression is 3, and the constant term in the second expression is 2.
Adding the constants, we get 3 + 2 = 5.
Combining the coefficients and constant terms, the sum of Carlos's expressions is 11p + 5.
So, Jon's sum is 7p + 3, and Carlos's sum is 11p + 5.