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A rideshare app charges $2 per trip plus $0.4 per mile…

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A rideshare app charges $2 per trip plus $0.4 per mile. A competitor charges $1 for the first 6 miles plus $0.5 per mile for every additional mile. For what length trip would the two services charge the same amount?

A. 10 miles
B. 18 miles
C. 20 miles
D. 40 miles

Can you craft an algebraic equation to solve this directly – or is plugging in the answers the way to go?

Mike McClenathan

A vending machine sells sodas for $2 each, storing the money inside. On Monday, the vending machine has 40 sodas in it and it contains $30. Write a function equation that gives the number of dollars the vending machine has, d, in terms of how many sodas the vending machine has, s.

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d = 30 + 2(40 – s) The machine begins the day with $30 inside, so that’s the “30 +” part. Easy enough. The variable s is defined as how many sodas the machine has in it, but what we really care about is how many sodas are sold. We know the machine begins the day with (more…)

Mike McClenathan

Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

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You can make two equations here. First, you know the total number of marbles is 103, so: The second equation is more complicated, so let’s do it in parts. First, he gives away 15 red marbles, so he should have r – 15 left. He gives away 2/5 of his blue marbles, so he should have (more…)

Mike McClenathan

Tariq and Penelope baked cookies and brownies for a school bake sale. Tariq made 30 brownies per hour, and Penelope made 48 cookies per hour. If the students worked for the same amount of time and produced 312 treats altogether, for how many hours did they work? Could you please include any tips you have on how to deal with these sort of problems? I’m usually stuck on these

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This question comes from my own book, so my tips on how to deal with these can be found in the same chapter. The main key to getting it right is making sure you translate the words into math correctly. Note that although the question tells you that Tariq makes brownies and Penelope makes cookies, (more…)

Deleted User

Pilar is a salesperson at car company…

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Pilar is a salesperson at car company. Each car costs at least $15,000. For each car she sells, she gets 6% commission of the amount by which selling price exceeds $10,000. If Pilar sells a car at d dollars, which function gives her the commission in dollars on sale?
A) C(d)=0.06(d-10000)
B) C(d)=0.06(d-15000)
C) C(d)=0.06(10000-d)

Mike McClenathan

Hey! I stumbled upon this problem while practicing for the SAT. The boiling point of water at sea level is 212 degrees Fahrenheit. For every increase of 1,000 feet above sea level, the boiling point of water drops approximately 1.84 Fahrenheit. Which of the following equations gives the approximate boiling point B, in Fahrenheit, at h feet above sea level? A) B = 212 – 1.84h B) B = 212 – (0.00184)h C) B = 212h D) B = 1.84(212) – 1,000h Can you please help me? Thank you!

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One way to make sure you get questions like these right is to plug in some values to see which equation makes sense. For example, you might choose to plug in 0 for h here because you know that at zero feet above sea level the boiling point should be 212° F. Choices C and D (more…)

Deleted User

Lisa gives her little brother Sam a 15-second (sec) head start in a 300-meter (m) race…

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This no-calculator prompt is from the Daily Practice app:

Lisa gives her little brother Sam a 15-second (sec) head start in a 300-meter (m) race. During the race, Sam runs at an average speed of 5 m/sec and Lisa runs at an average speed of 8 m/sec, not including the head start.

Which of the following best approximates the number of seconds that had passed when Lisa caught up to Sam?

A. 5
B. 25
C. 40
D. 55