How to solve a SAT Math Heart of Algebra problem
Heart of Algebra section in SAT Math tests your ability to solve problems making use of your knowledge of setting up equations in mathematical expressions with one or two variables. The equations may have an equality or an inequality sign. The questions may involve a practical problem wherein a relationship between different variables is presented. The expectation is for the students to convert the problem to a mathematical expression. Additionally, some problems may involve data presentation in graphical figures. One or more questions may be asked which test the ability to understand data presented in graphical form and arrive at the required solution.
Some of such questions in SAT Math Heart of Algebra section will feature multiple-choice and student produced response question types.
A sample question from the SAT Math Heart of Algebra section.
The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
Select an Answer
This is one of the sample questions from the collegeboard website
Hmm. It indicates the question is easy. The explanation is painfully wordy and often confusing. Not so if you are a bright student. Then possibly this website is not for u. Or maybe, if you stick around you may get some handy tips for u to succeed in getting 800 in your SAT. What. You think that’s impossible. Nothing is impossible.
Lets see how we can solve this problem.
Lets read each line carefully.
The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg).
Think: That means for every 20 year old the minimum calcium he needs to take in his body is 1000 mg.
Ok. That was easy.
Lets go to the second line.
One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium.
Think: Why this information. Well. The 20 year dude needs calcium. He gets it through milk and juice. Makes sense. So every cup of milk he takes he gets 299 mg of Calcium. Fine. And every cup of juice he takes he gets 261 mg of calcium. But is that enough. Do mental math. 299 + 261 or maybe approximately 300 + 300 = 600 mg of calcium. That’s not enough.
So the next line.
. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
Hmm. So he may drink more than 1 cup of milk and more than 1 cup of juice.
If he drinks 2 cups of milk, he gets 299+299 = 2*299 mg of calcium
If he drinks 3 cups of milk, he gets 299+299+299 = 3* 299 mg of calcium
If he drinks M cups of milk, he gets 299 + 299 + .. m times i.e. m*299 mg of calcium
Same logic for cups of juice,
If he drinks j cups of juice, he gets, 261 + 261 + j times i.e. J*261 mg of calcium.
Add both together, the total calcium intake is 299m + 261J.
This total should be either equal to or greater than the minimum required daily intake
Therefore, 299m+261J ≥ 1000.
Hence the right answer is option (A).
Phew!! We went through this in detail. Probably took you more than 3 minutes to read. But wait, you don’t have that much time to give to each question.
Yes, I know. But what we did here is just went through the process of solving the problem thoroughly. If you get used to this, you should be able to solve this problem in not more than 20 seconds. WHAT!!. Yes I am right. The key to preparing for SAT math exam is not just practice, it’s to master the process of reasoning.
Read through the information. Each line has important information. The key is to connect the informations together.
Help yourselves get better scores in SAT Math
There is no alternative to practicing. Practising in assimilating information in each line of a problem.
So good luck. Let me know if you need help and give me any problem you have difficutly solving or understanding and I will solve it along with clearing concepts along the way. Guaranteed.
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