Respuesta :
Answer: Apple Cheesecakes cost 17 dollars
Pecan Cheesecakes costs 5 dollars
Step-by-step explanation:
We first set
Pecan =p
Apple = a
So we can make the equations necessary to solve this equation.
Jasmine: 2p+8a=146
Brenda: 4p+7a=139
We can solve this by using Elimination Method:
Multiply Jasmine's equation by two to get：
4p+16a=292
From there we can subtract that equation from Brenda's to get rid of the p variable.
Once you subtract them. You should get:
9a= 153
Divide it by 9 to get：
a = 17
Now that we have the a variable, we can plug it in to any of the equations to solve for p. For this example, I'll plug it into Jasmine's.
2p+8(17)=146
2p+136=146
2p=10
p=5
So we now know that Pecan costed 5 dollars per cheesecake and Apples costed 17 dollars per cheesecake
Answer:
Cost of one pecan cheesecake = $5
Cost of one apple cheesecake = $17
Step-by-step explanation:
Let's denote the cost of one pecan cheesecake as [tex]\sf P[/tex] and the cost of one apple cheesecake as [tex]\sf A[/tex].
According to the given information:
Jasmine sold 2 pecan cheesecakes and 8 apple cheesecakes for a total of $146.
This can be expressed as an equation:
[tex]\sf 2P + 8A = 146 [/tex]
Brenda sold 4 pecan cheesecakes and 7 apple cheesecakes for a total of $139.
This can be expressed as another equation:
[tex]\sf 4P + 7A = 139 [/tex]
Now, we have a system of two equations:
[tex]\sf \begin{cases} 2P + 8A = 146 \\ 4P + 7A = 139 \end{cases} [/tex]
We can solve this system of equations to find the values of [tex]\sf P[/tex] and [tex]\sf A[/tex].
Let's multiply the first equation by 2 to make the coefficients of [tex]\sf P[/tex] in both equations the same:
[tex]\sf \begin{cases} 4P + 16A = 292 \\ 4P + 7A = 139 \end{cases} [/tex]
Now, subtract the first equation from the second:
[tex]\sf 4P + 16A - 4P- 7A = 292 - 139[/tex]
[tex]\sf 9A = 153 [/tex]
Divide by 9:
[tex]\sf \dfrac{ 9A }{9}= \dfrac{153 }{9}[/tex]
[tex]\sf A = 17 [/tex]
Now that we have the value for [tex]\sf A[/tex], substitute it back into one of the original equations.
Let's use the first one:
[tex]\sf 2P + 8(17) = 146 [/tex]
[tex]\sf 2P + 136 = 146 [/tex]
Subtract 136 from both sides:
[tex]\sf 2P + 136 -136 = 146-136 [/tex]
[tex]\sf 2P = 10 [/tex]
Divide by 2:
[tex]\sf \dfrac{ 2P}{2} = \dfrac{10 }{2}[/tex]
[tex]\sf P = 5 [/tex]
So, the cost of one pecan cheesecake ([tex]\sf P[/tex]) is $5, and the cost of one apple cheesecake ([tex]\sf A[/tex]) is $17.
