1) maurice runs 5 km in 15 mins.
→ 5 km = 15 mins
→ 20 km = ? mins
we must try to find "?"
- this is pretty easy, i will show you both ways to solve this.
<u>first way</u>
-> 5 x 4 = 20. so, if you multiply 5 by 4, you must multiply 15 by 4 as well.
-> 15 x 4 = 60 mins or 1 hour.
<u>second way</u>
proportions!
- set two fractions equal to each other.
-> 5/20 = 15/x (x = ? , i just made it less confusing)
-> use cross multiplying. multiply x by 5, and 15 by 20.
-> now you have 5x = 300
divide 5 on both sides. now, you have x = 60 (minutes)
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2) this time, we can divide.
-> $12.80 for 8 pounds, divide 12.80/8 = $1.60 per pound
-> so, we have $1.60 per pound for 20 pounds.
-> 1.60 x 20 = $32 for 20 pounds
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3) wingspan of ghost bat = 2x + 10 (let x = wingspan of vampire bat)
-> a ghost bat is 25 inches in this case.
<u>equation</u>: 2x + 10 = 25
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4) true crab = 2x - 4 (let x = number of hermit crab legs, y = true crab legs)
-> the hermit crab has 6 legs. let's plug in 6 for x.
y = 2x - 4
y = 2(6) - 4 (do not add 2 and 6, multiply!)
y = 12 - 4
y = 8
the true crab has 8 legs.
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5) twice the sum of x and 5
-> "the sum" means to add = x + 5
-> now, twice means to multiply by 2.
2(x + 5)
! never do 2x + 5 unless it says "twice x plus 5"! these problems can be very confusing, you must add x + 5 first and then multiply.
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6) 12 yards of fabric for petra, each costume requires 1 1/2 yards
-> in this problem, we divide.
-> 12 ÷ 1 1/2
12 ÷ 3/2
12/1 ÷ 3/2
12/1 x 2/3
(the KCF rule is to keep the first fraction, change the sign, and flip the second)
12/1 x 2/3 = 12 x 2/ 1 x 3 = 24/3 = 8 costumes
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7) a bag of potatoes = 4 1/2 pounds
first meal: 1 2/3 pounds eaten
second meal: 1 3/4 pounds are eaten
-> i'd rather add the first meal and second meal, then subtract it from 4 1/2
1 2/3 + 1 3/4
- we need a common denominator for 3 and 4 = 3 x 4 = 12.
1 2/3 + 1 3/4 -> 1 8/12 + 1 9/12
(when multiplying, multiply the numerator with it!)
1 8/12 + 1 9/12 = 1 17/12 = 2 5/12
-> now, we subtract 2 5/12 from 4 1/2
4 1/2 - 2 5/12
-> for the common denominator, we don't have to multiply 12 and 2 because 2 is already a factor of 12.
4 1/2 - 2 5/12 = 4 6/12 - 2 5/12 = 2 1/12
2 1/12 pounds of potatoes left in the bag
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8) michigan high: 101 ° F
michigan low: -32 ° F
difference = subtraction
-> 101 - - 32
(we have double negatives now! double negatives = positive!)
-> 101 - - 32 = 101 + 32 = 133
the difference is 133 ° F.
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9) your score: -200
lost final: lost 500 points, -500
which does not represent final score?
-> <u>correct equation =</u> -200 - 500
we find the opposite, so the answer is -200 + 500
✧ hope this helped! good luck on your exam and do well!
- aure
