a punch recipe that serves 24 people clothes for four leaders of lemon-lime soda,2 pints of sherbet and 6 cups of ice how much o
2 answers:
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Answer:
12. Option b: 20 is the correct answer.
13. Option a: A rose costs $1 more than a daisy is the correct answer.
Step-by-step explanation:
12. Given that:
15x+10y=700 Eqn 1
x+y=60 Eqn 2
To find x, we will eliminate y be multiplying Eqn 2 by 10
10(x+y=60)
10x+10y=600 Eqn 3
Subtracting Eqn 3 from Eqn 2
(15x+10y)-(10x+10y)=700-600
15x+10y-10x-10y=100
5x=100
Dividing both sides by 5
Hence,
Option b: 20 is the correct answer.
13. Given that:
5x+4y=32 Eqn 1
x+6y=22 Eqn 2
Multiplying Eqn 2 by 5
5(x+6y=22)
5x+30y=110 Eqn 3
Subtracting Eqn 1 from Eqn 3
(5x+30y)-(5x+4y)=110-32
5x+30y-5x+4y=78
26y=78
Dividing both sides by 26
Putting y=3 in Eqn 2
x+6(3)=22
x+18=22
x=22-18
x=4
Hence,
Option a: A rose costs $1 more than a daisy is the correct answer.
All the answers to the given parts are mentioned below -
<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
We can write the proportional relationship as -
y = kx
Now, from the given information, we can write -
2 scoops need 0.5 gallon of water
6 scoops need 1.5 gallon of water
So -
k = 2/0.5
k = 2/(1/2)
k = 2 x 2 = 4
Equations that represents the relationship can be written as -
y = 4x + c
Now, 2 scoops need 0.5 gallon of water.
2 = 4 x 1/2 + c
2 = 2 + c
c = 0
So, the equation will be y = 4x.
Graph of y = 4x is attached at the end.
For 10 scoops of water -
10 = 4x
x = 2.5 gallons of water is needed.
Therefore, all the answers to the given parts are mentioned above.
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