What is Mary's age?

Question

Mary is three less than twice Mark's age. Their combined age is 21. How old is Mary?

Answer 1

You have two unknown ages here, two variables: Mary's age and Mark's age. You also have two statements that give you information about the ages, which you can turn into two equations. First, you will want to choose a variable to stand for Mary's age, maybe "x." And you will need to assign a variable for Mark's age, maybe "y."

Now you have to turn the words into an equation. Start with the second sentence that says their combined age is 21. How do you show in mathematical terms that you are combining two different things? Adding! You have to add Mary plus Mark to find their combined age. So your first equation should reflect Mary's age (x) being added to Mark's age (y) being equal to 21.

Now go back to the first sentence. This also needs to be turned into an equation. Any time you see the word "is" means that you use the equals sign (=). So Mary's age = three less than twice Mark's age. Now, let's address the "three less than." What math can you do that will show less than: addition, subtraction, multiplication, or division? The answer here is subtraction. When you subtract, you are showing less than. So you will be subtracting 3. The second part says "twice Mark's age." What math can you do that shows twice: addition, subtraction, multiplication, or division? The answer here is multiplication. Twice is another word for saying "two times." Times is another way to say multiplication, or multiply. So, twice means we multiply by 2. Since we decided Mark's age would be represented by a "y," you would show 2 times y as "2y." Now, put it all together, three less than twice Mark's age is 2y - 3. Put in your equal sign and Mary's age (x) and you have an equation.

Now that you have two equations and two variables, you can solve this. One way to solve it is to take the easiest of the equations (their combined age is 21) and use algebra to move one of the variables to one side of the equation on it's own, so you have x = ... or y = ... I think the easier way for this problem is to isolate the variable y on it's own. To do that, you will have to subtract x on both sides. Remember, whatever you do to one side of the equation you must do to the other side of the equation as well. So if you subtract x from itself, you get zero, and are left with y alone on one side of the equation. The other side of the equation that used to just be "21" will now show "21-x" since you subtracted x on both sides.

Now you have an equation where y = ... and y is alone on one side if the equation. Use this to plug it into the other equation you made (Mary is three less than twice Mark's age). Re-write that equation, but this time instead of writing "y," replace it with "21-x." Now you have an equation that has one variable and you can finally solve it! Remember the rules of equations, you have to do math in the correct order. Parenthesis first, then multiplication and division, then subtraction and addition. Once you have simplified your equation, you will be able to solve for x, and find Mary's age.