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Math Problem Monday - Oct 30th, 2017 | Mathnasium Livermore, CA

Oct 30, 2017

Lower Elementary
Question: Aaron, Paul, and Bethany went fishing. Aaron caught 2 fish, Paul caught 3 fish, and Bethany caught twice as many fish as Paul. Altogether, how many fish did they catch?
Answer: 11 fish
Note: Bethany caught twice as many as Paul. Since Paul caught 3 fish, then Bethany caught 6 fish.
So,
2 fish + 3 fish + 6 fish = 11 fish

Upper Elementary
Question: Cameron collects baseball cards. Unfortunately Cameron lost half of his cards, but after searching for them he found half of the cards he lost. If Cameron had 128 before he lost any, how many cards does he have now?
Answer: 96 cards
Note: Cameron lost half of his 128 baseball cards.
Half of 128 = half of 100 + half of 20 + half of 8 = 50 +10 + 4 = 64
After losing 64 cards, Cameron now only has 64 cards, but then he found half of the cards he lost.
Half of 64 = half of 60 + half of 4 = 30 + 2 = 32
He had 64 cards and now found 32.
64 + 32 = 96

Middle School
Question: Jeremy paid $350 for his round trip airline ticket to a 5-day basketball camp. If he spent a total of $855 to go camp, how much did the basketball camp cost per day?
Answer: $101
Note: Letting x equal how much Jeremy paid per day he was at camp we can rewrite the problem in an algebraic equation.
5x + 350 = 855
Solving for x,
5x = 505
x = 101
This problem can be solved using strictly number sense by first subtracting out the $350 spent for the plane ticket from the total $855 spent on the entire trip ($855 – $350 = $505). Because he spent 5 days at basketball camp, we divide $505 by 5 showing he spent $101 per day at camp.

Algebra and Up
Question: Two cars leave from the same location headed in opposite directions. Car 1 travels at 65 mph and car 2 travels at 75 miles per hour. If car 2 left 1 hour after car 1, how many hours would it take for the two cars to be 325 miles apart? Round your answer to the nearest tenth.
Answer: About 2.9 hours
Note: This problem is solved by using the formula d = rt for both cars.
Car 1:
d1 = r1t1 = 65t1
Car 2:
d2 = r2t2 = 75t2
From the problem we know that car 2 left one hour after car 1 so we rewrite t2in terms of t1.
t2 = t1 – 1
Substituting in for t2,
d2 = 75(t1 – 1) = 75t1 – 75
Because we are trying to find how many hours it takes to for car 1 and car 2 to be 325 miles apart we add d1 and d2 together and set it equal to 325.
d1 + d2 = 325
Substituting in for d1 and d2,
65t1 + 75t1 – 75 = 325
Solving for t1 give us our final answer,
t1 ≈ 2.9 hours