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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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GCF and LCM: word problems

Full solution

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 $T$ . We know that Mindy ate $3$ pieces and Troy ate $\frac{1}{4}$ of the total cake. Together, they ate $9$ pieces. We can set up the equation as follows: $\newline$ Mindy's pieces + Troy's pieces = Total pieces eaten $\newline$ $3 + \left(\frac{1}{4}\right)T = 9$
Isolate T: Now we need to solve for T. To do this, we'll isolate T on one side of the equation. We can subtract $3$ from both sides to get: $\newline$ $(\frac{1}{4})T = 9 - 3$ $\newline$ $(\frac{1}{4})T = 6$
Multiply by $4$ : Next, we'll multiply both sides of the equation by $4$ to solve for T: $\newline$ $4 \times (\frac{1}{4})T = 4 \times 6$ $\newline$ $T = 24$
Final Total: We have found that the total number of pieces of cake, $T$ , is $24$ . This means there were $24$ pieces of cake in all.

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