A jar contains only pennies, nickels, dimes, and quarters. There are 21 pennies, 26 dimes, and 15 quarters. The rest of the
2 answers:
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The cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7
<em><u>Solution:</u></em>
Let "c" be the cost of 1 chocolate cake
Let "v" be the cost of 1 vanilla cake
<em><u>Jenny sold 14 chocolate cakes and 5 vanilla cakes for 119 dollars</u></em>
Therefore, we can frame a equation as:
14 x cost of 1 chocolate cake + 5 x cost of 1 vanilla cake = 119
14c + 5v = 119 ------- eqn 1
<em><u>Natalie sold 10 chocolate cakes and 10 vanilla cakes for 130 dollars</u></em>
Therefore, we can frame a equation as:
10 x cost of 1 chocolate cake + 10 x cost of 1 vanilla cake = 130
10c + 10v = 130 -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Multiply eqn 1 by 2
28c + 10v = 238 ------ eqn 3
<em><u>Subtract eqn 2 from eqn 3</u></em>
28c + 10v = 238
10c + 10v = 130
( - ) --------------------------
18c = 108
c = 6
<em><u>Substitute c = 6 in eqn 1</u></em>
14(6) + 5v = 119
84 + 5v = 119
5v = 119 - 84
5v = 35
v = 7
Thus cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7
Answer:
Step-by-step explanation:
Let:
This is an exact differential equation because:
With this in mind let's define f(x,y) such that:
and
So, the solution will be given by f(x,y)=C1, C1=arbitrary constant
Now, integrate with respect to x in order to find f(x,y)
where g(y) is an arbitrary function of y
Let's differentiate f(x,y) with respect to y in order to find g(y):
Now, let's replace the previous result into :
Solving for
Integrating both sides with respect to y:
Replacing this result into f(x,y)
Finally the solution is f(x,y)=C1 :