b) This is a DIRECT PROPORTION because we can expect that the more mini cookies are baked, the more quantity of flour is needed (unless someone is a magician).
GIVEN:
1,000g : 2 minicakes
7 minicakes
EQUATION:
1,000 : 2 : N : 7
OR
Note: I always prefer to follow the order of the first ratio for the second ratio. That way it is easier for me to see things. In the word problem above, the order is
weight : quantity : weight : quantity
SOLUTION:
Since this is a DIRECT PROPORTION, we simply need to multiply the means and the extremes. If you preferred to use fraction form then simply cross multiply:
1000 : 2 : N : 7
2×N = 1,000×7
2N = 7,000
N = 3,500g
c) Still DIRECT PROPORTION. The longer the Earl drives, the farther he can get.
Note: Since it is similar to the previous word problem, then no need to discuss.
15 : 3 : N : 5
3N = 15 × 5
3N = 75
N = 25km
d) This is an INVERSE PROPORTION because the more workers there are, the shorter the time required to finish. Thus, it can be said that as the value of a (workers) increases, b (time) decreases and vice versa.
GIVEN:
2 workers : 4 weeks : N : 1 week
EQUATION:
Unlike direct proportion where we can simply multiply the means and extremes, for this I will use magic:
where
t is the unknown and its kind
k is the constant
n is the other variable
SOLUTION:
For purposes of clarification
2 workers : 4 weeks : N workers : 1 week
Since "workers" in the second ratio is the missing variable, it be the t. I will be assigning it as:
for the known worker in the first ratio. (2 workers)
for the unknown in the second ratio. (N workers)
for the other variable thingy in the first ratio. (4 weeks)
for the other variable thingy in the second ratio. (1 week)
Unknown and its kind will always be outside or on the left side of the equation.
onlyakem
e) PARTITIVE PROPORTIONS. Add all parts in the given ratio, divide to total amount given, multiply the value of each part to given ratio such that we get 3:4:5 = 12 parts
Answers & Comments
Answer:
a) skipped because already answered separately.
b) 3,500g
c) 25km
d) 8 workers
Step-by-step explanation:
b) This is a DIRECT PROPORTION because we can expect that the more mini cookies are baked, the more quantity of flour is needed (unless someone is a magician).
GIVEN:
1,000g : 2 minicakes
7 minicakes
EQUATION:
1,000 : 2 : N : 7
OR
Note: I always prefer to follow the order of the first ratio for the second ratio. That way it is easier for me to see things. In the word problem above, the order is
weight : quantity : weight : quantity
SOLUTION:
Since this is a DIRECT PROPORTION, we simply need to multiply the means and the extremes. If you preferred to use fraction form then simply cross multiply:
1000 : 2 : N : 7
2×N = 1,000×7
2N = 7,000
N = 3,500g
c) Still DIRECT PROPORTION. The longer the Earl drives, the farther he can get.
Note: Since it is similar to the previous word problem, then no need to discuss.
15 : 3 : N : 5
3N = 15 × 5
3N = 75
N = 25km
d) This is an INVERSE PROPORTION because the more workers there are, the shorter the time required to finish. Thus, it can be said that as the value of a (workers) increases, b (time) decreases and vice versa.
GIVEN:
2 workers : 4 weeks : N : 1 week
EQUATION:
Unlike direct proportion where we can simply multiply the means and extremes, for this I will use magic:
where
t is the unknown and its kind
k is the constant
n is the other variable
SOLUTION:
For purposes of clarification
2 workers : 4 weeks : N workers : 1 week
Since "workers" in the second ratio is the missing variable, it be the t. I will be assigning it as:
Unknown and its kind will always be outside or on the left side of the equation.
Let's now substitute:
2 workers =![\frac{k}{4 weeks} \frac{k}{4 weeks}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bk%7D%7B4%20weeks%7D%20)
2 =![\frac{k}{4} \frac{k}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bk%7D%7B4%7D%20)
k = 2 × 4
k = 8
Great. Now if k = 8, then