Mindy and Troy combined ate 9 pieces of wedding cake. Mindy ate 3 pieces of cake and Troy had (1)/(4) of the total cake. How many pieces of cake were there in all?

Set Up Equation: Let's denote the total number of pieces of cake as T. According to the problem, Mindy ate 3 pieces of cake, and Troy ate 1/4 of the total cake. Together, they ate 9 pieces. We can set up the following equation to represent this situation: Mindy's pieces + Troy's pieces = Total pieces eaten 3 + (1/4)T = 9Isolate Term: Now we need to solve for T. To do this, we'll first isolate the term containing T on one side of the equation. We can subtract 3 from both sides to get: (1/4)T = 9 - 3Perform Subtraction: Perform the subtraction on the right side of the equation: (1/4)T = 6Multiply Both Sides: To find T, we need to multiply both sides of the equation by 4 to cancel out the 1/4 on the left side: 4 * (1/4)T = 6 * 4Find Total: Perform the multiplication on both sides: T = 24

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Mindy and Troy combined ate 9 pieces of wedding cake. Mindy ate 3 pieces of cake and Troy had
(1)/(4) of the total cake. How many pieces of cake were there in all?

Mindy and Troy combined ate $9$ pieces of wedding cake. Mindy ate $3$ pieces of cake and Troy had $\frac{1}{4}$ of the total cake. How many pieces of cake were there in all?

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Grade 6

One-step inequalities: word problems

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Q. Mindy and Troy combined ate

9

pieces of wedding cake. Mindy ate

3

pieces of cake and Troy had

\frac{1}{4}

of the total cake. How many pieces of cake were there in all?

Set Up Equation: Let's denote the total number of pieces of cake as $T$ . According to the problem, Mindy ate $3$ pieces of cake, and Troy ate $\frac{1}{4}$ of the total cake. Together, they ate $9$ pieces. We can set up the following equation to represent this situation: $\newline$ Mindy's pieces + Troy's pieces = Total pieces eaten $\newline$ $3 + \left(\frac{1}{4}\right)T = 9$
Isolate Term: Now we need to solve for $T$ . To do this, we'll first isolate the term containing $T$ on one side of the equation. We can subtract $3$ from both sides to get: $\newline$ $(\frac{1}{4})T = 9 - 3$
Perform Subtraction: Perform the subtraction on the right side of the equation: $\frac{1}{4}T = 6$
Multiply Both Sides: To find $T$ , we need to multiply both sides of the equation by $4$ to cancel out the $\frac{1}{4}$ on the left side: $\newline$ $4 \times \left(\frac{1}{4}\right)T = 6 \times 4$
Find Total: Perform the multiplication on both sides: $\newline$ $T = 24$