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## A problem with one variable: How old is Al?Many single-variable algebra word problems have to do with the relations between different people's ages. For example:Al's father is 45. He is 15 years older than twice Al's age. How old is Al?We can begin by assigning a variable to what we're asked to find. Here this is Al's age, so let Al's age = x. We also know from the information given in the problem that 45 is 15 more than twice Al's age. How can we translate this from words into mathematical symbols? What is twice Al's age?
Well, Al's age is x, so twice Al's age is 2x, and 15 more than twice Al's age is
It's always a good idea to check our answer:
## Solving a problem using one or two variables: How old is Karen?We can solve this problem using either one or two variables:Karen is twice as old as Lori. Three years from now, the sum of their ages will be 42. How old is Karen?
We'll let Lori's age be x. We can set up a chart: now in 3 years Karen 2x 2x + 3 Lori x x + 3The sum of their ages in 3 years will be 42, so we have: (2x + 3) + (x + 3) = 42 3x + 6 = 42 3x = 36 x = 12If Lori is 12, Karen is 24; in three years they will be 15 and 27, and the sum of their ages will be 42. Two-variable solution:If we want to use two variables to express the given information, we will need two equations to solve for these variables. Here's an example: Start by assigning variables. We want to find Karen's age, so let's call that K. But we need a variable for Lori's age too, so we will call her age L.
We know that Karen is twice as old as Lori. Another way of saying this is that Karen's age is 2 times Lori's age. This gives us our first equation: We also know that:
- in three years the sum of Karen's and Lori's ages will be 42;
- in three years, Karen's age will be 3 more than it is now, or K + 3;
- the same is true of Lori's age: in three years; it will be L + 3.
Since the sum of the girls' ages in three years is 42, we have our second equation:
Now we have two equations in two variables:
- K = 2L
- K + L = 36
Since
Again, it's always a good idea to check our answer.
- Karen is supposed to be twice as old as Lori. Karen is 24; Lori is 12. Is 24 twice 12? Yes.
- In three years, the sum of Karen's and Lori's ages should be 42. In 3 years, Karen will be 24 + 3 = 27 years old. In 3 years, Lori will be 12 + 3 = 15 years old. Is the sum of 27 and 15 equal to 42? Yes.
We can see that we have found the correct answer. ## From the Dr. Math archives:-
Al and his father (one variable)
Age and Money (two variables) Finding Ages: Tot and Teen (three variables) How Old are Ben and Kris? (one or two variables) How Old Are John and Julia? (two variables) Finding Age in an Algebra Word Problem (three variables) Finding the Ages of the Farmer's Daughters How Old is Chris Now? The Youngest of the Tennis Players (five variables) |

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