Question

At a party, 35 people each had a piece of cake that was $ \dfrac{1}{{16}}$ of a cake. How many cakes were eaten at the party?

Answer 1

Hint: In order to determine the count of cakes eaten at the party, form a mathematical expression from the statement given in the question as the cake eaten by one person is $ 1$ person $ = \dfrac{1}{{16}}\left( {cake} \right)$ .So for 35 people multiply both sides with $ 35$ to get the required answer.

Complete step by step solution:
We are given a word problem and form this we have to form some mathematical expression to get the answer.
According to the question , 35 people were in a party and each one of them consumed exactly$ \dfrac{1}{{16}}$ the part of a cake .
If we try form a mathematical equation from the above statement , we get the quantity of cake consumed by 1 person in the party as
$ 1$ person $ = \dfrac{1}{{16}}\left( {cake} \right)$
Here $ \left( {cake} \right)$ represents a single quantity of cake
But We have 35 people in the party, so multiplying 35 on both sides of the above expression in order to maintain the balance of the equation.
$ 1 \times 35$ persons $ = 35 \times \dfrac{1}{{16}}\left( {cake} \right)$
Simplifying the above equation further, we get
$ 35$ persons $ = \dfrac{{35}}{{16}}\left( {cake} \right)$
$ 35$ persons $ = \left( {2 + \dfrac{3}{{16}}} \right)\left( {cake} \right)$
$ 35$ persons $ = 2\left( {cake} \right) + \dfrac{3}{{16}}\left( {cake} \right)$
From above we can conclude that the count of cake consumed by the 35 people in the party is equal to $ 2\,cakes + \dfrac{3}{{16}}\,of\,cake$
Therefore, the number of cakes eaten is equal to $ 2\,cakes + \dfrac{3}{{16}}\,of\,cake$

Additional Information:
Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value .
A algebraic expression can contain any number of variables generally we take 2-3 variables
Let assume a expression
$ 5x + 9 = 24$
It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $ x$ is the variable
5 is the coefficient of variable $ x$
And $ 24,9$ are the constants

Note: 1. Read the statement carefully in order to convert them into mathematical expressions.
2. In the solution, Cake represents a single unit of cake.
3. Questions from which we have to obtain the mathematical expression are known as word problems..