QuestionMindy and Troy ate 9 pieces of cake. Mindy had 3 pieces, Troy had $\frac{1}{4}$ of the total. How much is the total?

Studdy Solution

STEP 1

Assumptions1. Mindy ate3 pieces of the cake. . Troy ate $\frac{1}{4}$ of the total cake.
3. Mindy and Troy together ate9 pieces of the cake.

STEP 2

First, we need to express the number of pieces Troy ate in terms of the total number of pieces in the cake. We can do this by setting up the equation $roy's\, pieces = Total\, pieces \\times \frac{1}{4}$

STEP 3

We also know that the total pieces eaten by Mindy and Troy is9. So we can set up another equation $Mindy's\, pieces + Troy's\, pieces =9$

STEP 4

Substitute the expression for Troy's pieces from2 into the equation from3 $3 + Total\, pieces \\times \frac{1}{4} =9$

STEP 5

Rearrange the equation to isolate the term with the total pieces on one side $Total\, pieces \\times \frac{1}{4} =9 -3$

STEP 6

Calculate the right side of the equation $Total\, pieces \\times \frac{1}{4} =6$

STEP 7

To solve for the total pieces, divide both sides of the equation by $\frac{1}{4}$ $Total\, pieces = \frac{6}{\frac{1}{4}}$

STEP 8

Calculate the total number of pieces in the cake $Total\, pieces = \frac{6}{\frac{1}{4}} =24$ The total number of pieces in the wedding cake is24.

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QuestionMindy and Troy ate 9 pieces of cake. Mindy had 3 pieces, Troy had $\frac{1}{4}$ of the total. How much is the total?

Studdy Solution

STEP 1

Assumptions1. Mindy ate3 pieces of the cake. . Troy ate $\frac{1}{4}$ of the total cake.
3. Mindy and Troy together ate9 pieces of the cake.

STEP 2

First, we need to express the number of pieces Troy ate in terms of the total number of pieces in the cake. We can do this by setting up the equation $roy's\, pieces = Total\, pieces \\times \frac{1}{4}$

STEP 3

We also know that the total pieces eaten by Mindy and Troy is9. So we can set up another equation $Mindy's\, pieces + Troy's\, pieces =9$

STEP 4

Substitute the expression for Troy's pieces from2 into the equation from3 $3 + Total\, pieces \\times \frac{1}{4} =9$

STEP 5

Rearrange the equation to isolate the term with the total pieces on one side $Total\, pieces \\times \frac{1}{4} =9 -3$

STEP 6

Calculate the right side of the equation $Total\, pieces \\times \frac{1}{4} =6$

STEP 7

To solve for the total pieces, divide both sides of the equation by $\frac{1}{4}$ $Total\, pieces = \frac{6}{\frac{1}{4}}$

STEP 8

Calculate the total number of pieces in the cake $Total\, pieces = \frac{6}{\frac{1}{4}} =24$ The total number of pieces in the wedding cake is24.

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QuestionMindy and Troy ate 9 pieces of cake. Mindy had 3 pieces, Troy had 14\frac{1}{4}41​ of the total. How much is the total?

Studdy Solution

STEP 1

Assumptions1. Mindy ate3 pieces of the cake. . Troy ate 14\frac{1}{4}41​ of the total cake.3. Mindy and Troy together ate9 pieces of the cake.

STEP 2

First, we need to express the number of pieces Troy ate in terms of the total number of pieces in the cake. We can do this by setting up the equationroy′s pieces=Total piecestimes14roy's\, pieces = Total\, pieces \\times \frac{1}{4}roy′spieces=Totalpiecestimes41​

STEP 3

We also know that the total pieces eaten by Mindy and Troy is9. So we can set up another equationMindy′s pieces+Troy′s pieces=9Mindy's\, pieces + Troy's\, pieces =9Mindy′spieces+Troy′spieces=9

STEP 4

Substitute the expression for Troy's pieces from2 into the equation from33+Total piecestimes14=93 + Total\, pieces \\times \frac{1}{4} =93+Totalpiecestimes41​=9

STEP 5

Rearrange the equation to isolate the term with the total pieces on one sideTotal piecestimes14=9−3Total\, pieces \\times \frac{1}{4} =9 -3Totalpiecestimes41​=9−3

STEP 6

Calculate the right side of the equationTotal piecestimes14=6Total\, pieces \\times \frac{1}{4} =6Totalpiecestimes41​=6

STEP 7

To solve for the total pieces, divide both sides of the equation by 14\frac{1}{4}41​Total pieces=614Total\, pieces = \frac{6}{\frac{1}{4}}Totalpieces=41​6​

STEP 8

Calculate the total number of pieces in the cakeTotal pieces=614=24Total\, pieces = \frac{6}{\frac{1}{4}} =24Totalpieces=41​6​=24The total number of pieces in the wedding cake is24.

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QuestionMindy and Troy ate 9 pieces of cake. Mindy had 3 pieces, Troy had $\frac{1}{4}$ of the total. How much is the total?

Assumptions1. Mindy ate3 pieces of the cake. . Troy ate $\frac{1}{4}$ of the total cake.
3. Mindy and Troy together ate9 pieces of the cake.

First, we need to express the number of pieces Troy ate in terms of the total number of pieces in the cake. We can do this by setting up the equation $roy's\, pieces = Total\, pieces \\times \frac{1}{4}$

We also know that the total pieces eaten by Mindy and Troy is9. So we can set up another equation $Mindy's\, pieces + Troy's\, pieces =9$

Substitute the expression for Troy's pieces from2 into the equation from3 $3 + Total\, pieces \\times \frac{1}{4} =9$

Rearrange the equation to isolate the term with the total pieces on one side $Total\, pieces \\times \frac{1}{4} =9 -3$

Calculate the right side of the equation $Total\, pieces \\times \frac{1}{4} =6$

To solve for the total pieces, divide both sides of the equation by $\frac{1}{4}$ $Total\, pieces = \frac{6}{\frac{1}{4}}$

Calculate the total number of pieces in the cake $Total\, pieces = \frac{6}{\frac{1}{4}} =24$ The total number of pieces in the wedding cake is24.