# Mindy and Troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and Troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) left there were in total. what is the total number of pieces of cake?

Apr 11, 2018

24 pieces total,
R = 3tot/4-3

#### Explanation:

m = Mindy
t = troy
tot = total number of pieces
R = remaining amount

So we know that Mindy and ate a combined number of thirteen pieces:

$m + t = 9$

We also know Mindy ate 3:
$m = 3$
and Troy ate $\frac{1}{4}$ of the total number:
t = tot$/ 4$

so after combining:

3 + tot/4 = 9

now we solve for tot:

tot/4 = 6
tot = 24

So there is a total of 24 pieces.

R = tot - (tot/4+3)

R = 3tot/4-3

R = 15

Apr 11, 2018

First, we need to find out how many pieces of cake Troy ate.

If Mindy and Troy at $9$ pieces, and Mindy at $3$ of them, Tony must have eaten $6$ pieces. If $6$ pieces of cake is $\frac{1}{4}$ of the whole, then we now know everything we need to write an equation:

$c = \left(4 \times 6\right) - 9$

where cake is equal to $4$ quarters of $6$ pieces of cake (6 + 6 + 6 + 6) without the $9$ pieces Mindy and Troy ate.

So, $c = 24 - 9 = 15$

There $15$ pieces of cake leftover.

The total number of pieces of cake is $24$