Converting Word Problems into Equations
In order to solve word problems, it is helpful to convert them into equations. This video gives a detailed example of how to convert a word problem into equations.
Converting Words to Equations
In order to solve this word problem here, we first need to convert these word phrases into equations. From the first sentence we know that Rick’s age is 5 more than 4 times his daughter Amy’s age, so we’ll write an equation with Rick’s age represented by R and Amy’s age represented by A.
We’re told that Rick’s age is 5 more than, or if we subtract 5, is equal to 4 times his daughter’s age, 4A. We could also have written this as Rick’s age is 5 more than 4 times his daughter’s age, so either one of these equations is an acceptable way to write that first sentence.
The second sentence tells us that Rick was 29 when Amy was born, or Rick is 29 years older than Amy, so Rick’s age minus 29 equals Amy’s age, or Rick’s age is Amy’s age plus 29. Now if we want to go ahead and solve these, we can see that we have two equations that are both equal to R, so we can rewrite this as a single equation, 4A plus 5 is equal to R, and A plus 29 is equal to R.
Now we can solve this equation by subtracting A from both sides and subtracting 5 from both sides. That gets rid of those As and those 5s, and what we’re left with is 3A equals 24. If we divide both sides by 3, we get A equals 8, so Amy is eight years old.
Now, we can plug Amy’s age back into any one of these equations to find Rick’s age. The easiest one, though, is going to be this one right here, so we’ll plug in 8 for A, we get R equals 8 plus 29, or R equals 37, so Rick is 37 and Amy is 8.