News from Mathnasium of Middletown KY
Problem of the Week 06-27-16
Jun 29, 2016
Question: There are 30 rows of passenger seats on an airplane. The seats in each row are labeled A, B, C, D, and E. How many passengers can the plane hold?
Answer: 150 passengers
Solution: If there are 30 rows of seats and there’s an A, B, C, D, and E seat in each row, then there are 30 A seats, 30 B seats, 30 C seats, 30 D seats, and 30 E seats. That means that there are 30 + 30 + 30 + 30 + 30 = 150 seats.
Question: Amelia is taking a train to Chicago. The trip is 7 hours long, and the train travels a total of 560 miles. What is the rate of the train’s speed in miles per hour?
Answer: 80 miles per hour
Solution: To find the number of miles the train can travel per hour, we need to divide the number of miles by the number of hours: 560 miles ÷ 7 hours = 80 mph
Question: Jamie is filling the gas tank of his car. The tank holds 11 gallons of gas and is half full when Jamie pulls into the gas station. If he fills the tank completely and the gas costs $2.988 (2 dollars, 98 cents, and 8 mills) per gallon, how much does Jamie spend on gas?
(Hint: The smallest unit of currency that a gas station can charge is a cent, so remember to round!)
Solution: Half of 11 is 51/2, so Jamie will need to buy 51/2 gallons of gas to fill the tank. The price of 51/2 gallons of gas is 5.5 × 2.988 = 16.434, but the gas station can’t charge 0.4 cents, or 4 mills, so we’ll need to round that price down to $16.43.
Algebra and Up:
Question: Graph the following inequality on the plane below: 3x – 2y < 9
Solution: To graph a line, we need two points. The two easiest points to find on this line are its intercepts, which we can find by plugging in zero for x, then y. By doing this, we find that the y-intercept is (0, –4.5) and the x-intercept is (3, 0). We connect these points—which should be empty points—using a dashed line because none of the points on the line satisfy the inequality. To find out which side to shade, we can plug in a point (let’s use 1,1 for simplicity’s sake) and see if it satisfies the inequality or not. 3(1) – 2(1) < 9, so the side of the line with that point gets shaded in; everything on that side satisfies the inequality.
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