37 1/2 divided by 2 1/2=15
Marco can fill 15 cups with juice samples.
Check:
2 1/2x15=37 1/2
( x + 1 )/ 3 = x + 2
Multiply 3 on both sides
x + 1 = 3x + 6
Subtract 6 on both sides
x - 5 = 3x
Subtract x from both sides
-5 = 2x
Divide 2 from both sides
x = -2.5
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: 
where c is the total amount in the glass. This means that: 
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: 
and that: 
.
So if we're going to add the two glasses, we simply add the two sides, and get: 
. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: 
Now we can add like terms to get the equation: 
. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Answer:
4
Step-by-step explanation:
Multiply both sides by 7.
5s+8=28
Subtract 8 from both sides.
5s=20
Divide 5 from both sides,
s=4
Answer:
42 child and 70 adult
Step-by-step explanation:
Let a = number of adult tickets
c = number of child tickets
a+c = 112
2.25a + 1.75c = 231
Solve the first equation for a
a = 112-c
Substitute this into the second equation
2.25(112-c) + 1.75c = 231
Distribute
252 - 2.25c +1.75c = 231
Combine like terms
252 -.5c = 231
Subtract 252 from each side
252-252 -.5c = 231-252
-.5c = -21
Divide each side by -.5
-.5c/-.5 = -21/ -.5
c = 42
Now can find a
a = 112-c
a = 112-42
a = 70
