SAT Math: Practice Questions-Heart of algebra-Understanding linear relationships

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Question

 \(11.5x+3.5y=265\)

A person used a total of 265 kilocalories (kcal) while walking and running on a treadmill. Running at a constant rate required 11.5 kcal per minute, and walking at a constant rate required 3.5 kcal per minute. The relationship between the number of minutes running, \(x\), and the number of minutes walking, \(y\), is given by the equation shown. If this person ran for 20 minutes, how many minutes did this person walk?

  1. 35
  2. 29
  3. 17
  4. 10
Answer/Explanation

Ans: D

Question

A calf, the offspring of a cow, weighed 62 pounds at birth. The calf is expected to gain 2 pounds every day for the first 2 years of its life. For this time period, which of the following types of functions best models the weight of the calf as a function of time?

  1. Increasing linear
  2. Decreasing linear
  3. Increasing exponential
  4. Decreasing exponential
Answer/Explanation

Ans: A

Question

Ivan plans to save up to \($\)5 per day. The graph shows the possible amounts of money \(y\), in dollars, he saved after \(x\) days. Which ordered pair \((x,y)\) represents a possible amount of money \(y\), in dollars, he saved after \(x\) days? 

  1. (18,50)
  2. (12,75)
  3. (8,100)
  4. (4,125)
Answer/Explanation

Ans: A

Question

It took 20 minutes for a jet to climb from a starting altitude of 10,000 feet to a final altitude of 30,000 feet. If the jet climbed at a constant rate, what was its altitude, in feet, 14 minutes after the climb began?

  1. 14,000
  2. 21,000
  3. 24,000
  4. 28,000
Answer/Explanation

Ans: C

Question

4\(T\)-8\(D\)=12\(H\)

The given equation can be rewritten as \(T\)=\(a\)\(D\)+\(b\)\(H\), where \(a\) and \(b\) are constants. What is the value of \(a\)?

Answer/Explanation

Ans: 2

Question

At sea level, the boiling point of water is 212 degrees Fahrenheit (°F). For every 500-foot increase in elevation above sea level, the boiling point of water decreases by about 1°F. Which equation models water’s boiling point \(y\), in °F, in terms of \(x\), the elevation, in feet above sea level?

  1. \(\frac{-1}{500}x+212\)
  2. -500\(x\)+212
  3. \(\frac{1}{500}x-212\)
  4. 500\(x\)-212
Answer/Explanation

Ans: A

Question

20\(d\)+0.7\(m\)=235
Shelly spent \($\)235 to rent a moving van. The equation above shows the relationship between the number of days she rented the van, \(d\), and the number of miles she drove the van, \(m\). If she rented the van for 3 days, how many miles did she drive the van?

  1. 118
  2. 250
  3. 307
  4. 421
Answer/Explanation

Ans: B

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