SAT Math Question (5) - System of Equations

Good News Steemers!

I have a new SAT question for you! This is a classic systems of equations question. You have to remember that just because the numbers are large does not make it a harder question! They could do this on the real SATs to prevent students from using the good old "guess and check".

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Question

Jack is a well-off teacher. He has been teaching high school for a year and has made millions of dollars. Now, Jack wants to pay for all pens and pencils teachers use in the state of Florida for the next school year. He goes online and finds out he can buy the most expensive pencils for 1.28 each and the most expensive pens for 3.99 each. Jack is a firm believer that students should use pencils, so he buys a significant amount more than the pens. All in all, he bought 1096894 pens and pencils for a total of $2545888.24. How many of each did he buy?

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Answer

Step 1: Take the important information out of the long BS story that you just read:

• Pencils are $1.28
• Pens are $3.99
• Total number of pens and pencils is 1096894
• Total price was $2545888.24

Step 2: Make two equations for the system (one for each unknown):
Call pencils N and pens P. This gives us two clear equations.

• Number of Pencils + Number of Pens = 1096894 ... N + P = 1096894
• Price of Pencils + Price of Pens = $2545888.24 ... 1.28N + 3.99P = 2545888.24

Step 3: Use algebra to solve (Substitution Method):
First, solve for a letter in one equation, say P in the first equation, so subtract N to the other side:

Then, plug that into the other equation and solve for N:

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