Final Answer:
To have a total of 140 ounces, you would need 70 ounces of dough and 70 ounces of sauerkraut.
Step-by-step explanation:
In order to determine the amount of dough and sauerkraut needed to achieve a total of 140 ounces, you can set up a simple algebraic equation. Let x represent the amount of dough in ounces and y represent the amount of sauerkraut in ounces. The sum of x and y should equal 140:
![\[x + y = 140\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/x9uq82fxph6nlw2sk6slt60np5nk89esls.png)
Since the question specifies that the total is made up of both dough and sauerkraut, the individual amounts of each ingredient should be equal. Therefore, you can express y in terms of x:
![\[y = x\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/isxi6ng2edycjjg4ig1f4ulpax43iur4yq.png)
Now, substitute this expression into the original equation:
![\[x + x = 140\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/5jdw49aq5jhgmxm3bnaheaaa11lgotcqhq.png)
Combine like terms:
![\[2x = 140\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/uwp2lqbugnfuv0vtid34q5ehw2c4eu2xpk.png)
Divide by 2 to solve for x:
![\[x = 70\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/mf4wmdrbzhgr95rzsdoclsg7dofye0dfef.png)
So, you would need 70 ounces of dough. To find the amount of sauerkraut, substitute this value back into the expression for y:
![\[y = 70\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/o18yov13a9g3efxdb8yv5k7pcwi3lnq3cd.png)
Hence, you would need 70 ounces of sauerkraut as well. The total sum of 70 ounces of dough and 70 ounces of sauerkraut equals the desired 140 ounces.