A coffee blender mixes 2 types of coffee. Type A costs $13 per kg and type B costs $18 per kg. How many grams of each type of coffee must be blended so that 1 kg costs $15?
can U explain where the one comes from
Well, let's take this coffee conundrum and brew up a solution! To make 1 kg of coffee that costs $15, we need to find the right blend of Type A and Type B coffee.
Let's assume we need x grams of Type A coffee and y grams of Type B coffee. Since we're blending 1 kg (or 1000 grams) of coffee, we have the equation x + y = 1000.
Now, we need to account for the cost of the blend. Type A coffee costs $13 per kg, so it would be $13/1000 grams per gram, making it 13/1000 dollars per gram. Similarly, Type B coffee costs $18 per kg, or 18/1000 dollars per gram.
Since we want the blend to cost $15 per kg, or $15/1000 dollars per gram, we can set up another equation: (13x + 18y)/1000 = 15/1000.
Are you ready for the punchline? Let's simplify the equation!
13x + 18y = 15... Wait, that's not very funny. Let's try again!
Knock-knock.
- Who's there?
Java.
- Java who?
Java little math problem to solve!
Now, let's solve the two equations simultaneously to find the values for x and y. I'll keep the math jokes coming while we work it out. Deal?
Setting up the equations:
x + y = 1000 (equation 1)
13x + 18y = 15000 (equation 2)
Let's use the first equation to express x in terms of y:
x = 1000 - y
Substituting x in the second equation:
13(1000 - y) + 18y = 15000
Simplifying:
13000 - 13y + 18y = 15000
Combining like terms:
5y = 2000
Dividing by 5:
y = 400
Now, substitute the value of y back into equation 1:
x + 400 = 1000
x = 600
Voila! To make 1 kg of coffee that costs $15, you'll need 600 grams of Type A coffee and 400 grams of Type B coffee. That should perk up your day!
To find out how many grams of each type of coffee must be blended, we can set up a system of equations.
Let's assume x grams of type A coffee and y grams of type B coffee are mixed.
The cost of type A coffee is $13 per kg, which means it costs $13/1000 grams = $0.013 per gram.
Similarly, the cost of type B coffee is $18/1000 grams = $0.018 per gram.
The total cost of the blend should be $15 per kg, which means $15/1000 grams = $0.015 per gram.
We can now set up the following equations:
Equation 1: x + y = 1000 (since we're considering 1 kg of coffee, which is equivalent to 1000 grams)
Equation 2: ($0.013)(x) + ($0.018)(y) = ($0.015)(1000)
Simplifying Equation 2, we get: 0.013x + 0.018y = 15
Now we have a system of equations to solve simultaneously. Here's one way to do that:
1. Solve Equation 1 for x: x = 1000 - y
2. Substitute the value of x into Equation 2: 0.013(1000 - y) + 0.018y = 15
3. Simplify and solve for y: 13 - 0.013y + 0.018y = 15
Combine like terms: 0.005y = 2
Divide both sides by 0.005: y = 400
Now that we have the value of y (grams of type B coffee), we can substitute it back into Equation 1 to find x:
x + 400 = 1000
x = 1000 - 400
x = 600
Therefore, to make 1 kg of coffee costing $15, you would need 600 grams of type A coffee and 400 grams of type B coffee.
a,b means the weight of each .
13a+18b=(1)15
and a+b=1
multiply second equation by13 and subtract it from the first
13a+18b=(1)15
13a+13b=13
and then
5b=2 or b= .4kg, and then a=.6kg
Let's assume that x grams of type A coffee and y grams of type B coffee are blended.
The cost of type A coffee per gram is $13/1000 = $0.013.
The cost of type B coffee per gram is $18/1000 = $0.018.
According to the given information, the average cost of the blend is $15 per kg, which is $15/1000 = $0.015 per gram.
We can set up two equations to represent the total cost and total weight of the blend:
Equation 1: 0.013x + 0.018y = 0.015(x + y)
Equation 2: x + y = 1000 (since 1 kg is equal to 1000 grams)
Now, let's solve this system of equations to find the values of x and y.
From Equation 2, we can rewrite it as x = 1000 - y and substitute it into Equation 1:
0.013(1000 - y) + 0.018y = 0.015(1000)
Simplifying this equation:
13 - 0.013y + 0.018y = 15
0.005y = 2
y = 2/0.005
y = 400
Substituting the value of y back into Equation 2:
x + 400 = 1000
x = 1000 - 400
x = 600
Therefore, to have a blend costing $15 per kg, you need to mix 600 grams of type A coffee with 400 grams of type B coffee.