Let’s look at some examples.

At a movie theater, a popcorn costs $2 more than a soda. If buying 2 popcorns and 4 sodas costs $28, how much do a popcorn and a soda together cost?

A) $4

B) $6

C) $10

D) $13

Looking at the first sentence, we could create an equation like

$$p=s+2\;\;\;\;\;\;or\;\;\;\;\;\;\;\;p-2=s$$

We use *p* instead of *x *here to make it very clear what the variable represents, *popcorn*. Also note that these are exactly the same equation, we can write it either way depending on what variable we want to isolate.

Looking at the second sentence, we can generate another equation.

$$2p + 4s = 28$$

Because we already have a variable isolated in the first equation, substitution will probably be much easier than elimination. Here we’ll substitute for *p*.

$$2(s+2)+4s=28\\2s+4+4s=28\\6s=24\\s=4$$

Now that we have *s*, we can plug it back into our original equation to find out that *p* is 6. Look closely at our answers! We have both 4 and 6 as answer choices, representing the price of soda and popcorn, but that is NOT what the question is asking for. We have to find the two of them added together to get answer C).

**TIP: Underline the final question in every math problem, this way you ensure that your eyes are reading closely what the question is actually asking for. The SAT loves to put the values for x and y in the answer choices, and then ask you what some combination of them is. Underline the actual question!**

In this next example, the answer choices are pairs of equations, so you can form your own equations, then look for the ones that match yours:

Mike’s Meatball Market sold 2,321 meatballs from Friday to Sunday. All the meatballs sold at Mike’s are either beef or turkey. Beef meatballs sell for $1.50 each, turkey meatballs sell for $2 each, and the total sales from beef and turkey meatballs was $3,876. If the number of beef meatballs sold is represented by *b*, and the number of turkey meatballs sold is represented by *t*, then which of the following systems of equations, if solved, would determine the number of each type of meatball sold?

A) \(1.5b+2t=3,876\\b+t=2,321\)

B) \(1.5b+2t=2,321\\b+t=3,876\)

C) \(2b+1.5t=3,876\\b–t=2,321\)

D) \(2b+1.5t=3,876\\b+t=2,321\)

First we should decide if it needs to be *b *+ *t* or *b *– *t, * and then if it should equal 2,321 or 3,876. We go back to the word problem, and see “Mike’s Meatball Market sold 2,321 meatballs from Friday to Sunday. All the meatballs sold at Mike’s are either beef or turkey.” We can paraphrase this as “they sold 2,321 beef and turkey meatballs combined”, or *b *+ *t* = 2,321. We can immediately rule out answers B) and C).

Now we look at the difference between the first equation in A) and D), and see that the *b* coefficients are different. Should it be 1.5*b * or 2*b* ? Going back to the words, we see “Beef meatballs sell for $1.50 each”. $1.50 times the number of beef meatballs is the same as 1.5*b* , so we now know the correct answer is A).

Login

Accessing this course requires a login. Please enter your credentials below!