18=12 C+13 S A batch of hard candy needs C gallons of corn syrup and S gallons of sucrose to create 18 pounds of sweetener as shown in the equation. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by 1 gallon?

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18=12 C+13 S A batch of hard candy needs  C gallons of corn syrup and  S gallons of sucrose to create 18 pounds of sweetener as shown in the equation. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by 1 gallon?

Bytelearn · Accepted Answer

Understand Equation: Let's first understand the equation given: 18 = 12C + 13S. This equation represents the total pounds of sweetener made from C gallons of corn syrup and S gallons of sucrose.Find C Increase: We need to find out how much C increases when S decreases by 1 gallon. Let's call the new amount of sucrose S - 1.Substitute S-1: Substitute S - 1 for S in the equation: 18 = 12C + 13(S - 1).Distribute 13: Now, distribute the 13 to both terms inside the parentheses: 18 = 12C + 13S - 13.Maintain Total Weight: We know that the original equation was 18 = 12C + 13S, so if we compare it with the new equation 18 = 12C + 13S - 13, we can see that the total pounds of sweetener should remain the same, which is 18 pounds.Isolate 12C Term: To keep the total at 18 pounds, we need to increase the amount of corn syrup to compensate for the decrease in sucrose. So, we add 13 to both sides of the new equation to isolate the 12C term: 18 + 13 = 12C + 13S.

$18=12 C+13 S$ $\newline$ A batch of hard candy needs $C$ gallons of corn syrup and $S$ gallons of sucrose to create $18$ pounds of sweetener as shown in the equation. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by $1$ gallon?

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18=12C+13S 18=12 C+13 S 18=12C+13S\newlineA batch of hard candy needs C C C gallons of corn syrup and S S S gallons of sucrose to create 181818 pounds of sweetener as shown in the equation. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by 111 gallon?

$18=12 C+13 S$ $\newline$ A batch of hard candy needs $C$ gallons of corn syrup and $S$ gallons of sucrose to create $18$ pounds of sweetener as shown in the equation. What is the increase in the amount of corn syrup in gallons if the amount of sucrose decreases by $1$ gallon?