In a restaurants kitchen, c cakes are made by adding s cups of sugar to a mix of eggs and butter. If s= 3c+5 how many more cups of sugar are needed to make one additional cake?
looks like 3 ... the slope of the line
Well, in the grand tradition of cooking and mathematics, let's mix things up a bit! If you have c cakes made with s cups of sugar, and s equals 3c+5, then we can substitute the s value into our equation.
So, s = 3c + 5. If we want to see how many more cups of sugar are needed to make one additional cake, let's consider that c value. If we increase c by 1, we need to find the value of s for that new number of cakes.
Now, let's solve for the new s value:
s = 3(c+1) + 5
s = 3c + 3 + 5
s = 3c + 8
Now, we just need to compare the two values of s:
s (for c cakes) = 3c + 5
s (for c+1 cakes) = 3c + 8
To find the difference, we subtract the first equation from the second:
(3c + 8) - (3c + 5) = 3c - 3c + 8 - 5
0 + 3 = 3
So, my friend, you need 3 more cups of sugar to make one additional cake. Just remember to keep things sweet and funny in the kitchen!
To find out how many more cups of sugar are needed to make one additional cake, we need to determine the amount of sugar required for making c cakes and then subtract the amount of sugar required for making (c - 1) cakes.
Let's start by finding the amount of sugar needed for making c cakes, given that s = 3c + 5.
Step 1: Substitute the value of s in terms of c into the equation.
s = 3c + 5
Step 2: Substitute c in relation to s.
s = 3(c - 1) + 5
Step 3: Simplify the equation.
s = 3c - 3 + 5
s = 3c + 2
We have now found the amount of sugar needed for making c cakes.
Next, we'll find the amount of sugar needed for making (c - 1) cakes.
Step 4: Substitute (c - 1) in relation to s.
s = 3(c - 1 - 1) + 5
s = 3(c - 2) + 5
Step 5: Simplify the equation.
s = 3c - 6 + 5
s = 3c - 1
Now, let's calculate the difference between the two equations to find the additional cups of sugar needed for one more cake.
Step 6: Subtract the second equation from the first equation.
(3c + 2) - (3c - 1)
3c + 2 - 3c + 1
3c - 3c + 2 + 1
0c + 3
Therefore, to make one additional cake, you would need 3 more cups of sugar.
To find out how many more cups of sugar are needed to make one additional cake, we first need to determine the amount of sugar needed for one cake.
The given equation provides the relationship between the number of cakes (c) and the amount of sugar (s), with s = 3c + 5.
Now, let's substitute s = 3c + 5 into the equation. We have:
s = 3c + 5
= 3(1) + 5 (since we want to find the amount of sugar needed for one additional cake, so c = 1)
= 3 + 5
= 8
Therefore, to make one additional cake, we would need 8 cups of sugar.
So, the answer is 8 cups of sugar.