Use the information to write an equation with variables on both sides. Let x represent Kim’s age.
Bob is 4 years older than twice Kim’s age.
Paul is 1 year younger than 3 times Kim's age.
Bob and Paul are the same age.
Which equation can be used to determine Kim’s age, x, from the information about Bob and Paul?
4x + 2 = 3x + 1
4x + 2 = 3x + (–1)
2x + 4 = 3x + 1
2x + 4 = 3x + (–1)
Start by translating the information given into equations:
Bob is 4 years older than twice Kim's age: B = 4 + 2x
Paul is 1 year younger than 3 times Kim's age: P = 3x - 1
Bob and Paul are the same age: B = P
Substitute B for P (since they are the same) and simplify:
4 + 2x = 3x - 1
Now solve for x by isolating the variable on one side:
4 + x = -1
x = -5
Therefore, Kim is -5 years old, which does not make sense. So, there must be an error in the information given. The equation 2x + 4 = 3x - 1 is not needed or applicable in this situation.
Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step? Explain.
The first step in solving this equation is to simplify it by isolating the variable (x) on one side of the equal sign. To help Tucker decide on his first step, he should consider the coefficients of the x term.
On the left side of the equation, there are 5 positive x tiles and on the right side, there are 6 positive x tiles. If he subtracts 5 negative x tiles from both sides, he will have 5x on the left and 6x - 5x = x on the right side.
On the other hand, there is a constant term (3) on the left side and a constant term (1) on the right side of the equation. If he subtracts 1 negative unit tile from both sides, he will have 5x + 2 on the left side and 6x on the right side.
To choose the first step, Tucker should consider which approach simplifies the equation the most, as this will make the subsequent steps easier. In this case, subtracting 1 from both sides seems to be the easier way, because it results in a variable coefficient of 5 on one side and a variable coefficient of 6 on the other side. Subtracting 5 to both sides would result in the coefficients being 5 and 1, which is not as simple to work with.
Therefore, Tucker's first step should be to subtract 1 negative unit tile from both sides of the equation.
Let's break down the information given to determine the equation.
Bob is 4 years older than twice Kim's age:
Bob's age = 2x + 4
Paul is 1 year younger than 3 times Kim's age:
Paul's age = 3x - 1
Bob and Paul are the same age:
Bob's age = Paul's age
Now we can set up an equation using this information:
2x + 4 = 3x - 1
Therefore, the correct equation to determine Kim's age is:
2x + 4 = 3x - 1