Heidi T. answered • 12/03/19

MA in Mathematics, PhD in Physics with 7+ years teaching experience

Usually, as in this question, each sentence represents an equation. The first and second sentence represent two equations. You are looking for two integers (1st sentence), so give them names, say a and b, let a be the smaller integer and b the larger. The first sentence also gives you an equation: the sum of the two integers is 21. Sum tells you that you are adding the two integers, the word "is" usually means "equals"

1st equation is therefore: a + b = 21

The second sentence give another equation. To find this one, you need to "translate" a few more English words into math. The word "more" or phrase "more than" means you are adding two things together. Triple of any thing means three or three times (Triple Crown in horse racing = 3 "crown" races) the "square of " means that you are taking whatever follows to the second power, "is equal to" is exactly what it says.

Putting it together: "seven more than" (7 + ) "triple the square of the smaller integer" (3*(a^2)) "is equal to the larger integer" ( = b ) ==> your second equation is: 7 + 3(a^2) = b

Solve the first equation for either a or b and substitute into this second equation to produce an equation in one variable - solve for that variable, then you can use the first equation to get your second variable.

One thing I always recommend - is construct an "math-English" dictionary that has all the English words and phrases that mean some particular math operation. This can help in decoding word problems like this, and just the act of compiling it helps you learn what to look for as you read the problems.