Algebraic word problem, please answer with the equation and answer, thank you.

Question

Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly decided the rest among her children. Each child received two pieces. With how many pieces did she start?

Answer 1

In order to solve this problem we will have to break it into pieces and set up an Algebraic equation.

 

Here is what we know

aliyah took 10 pieces of candy 

she has four children

Each child got 2 pieces of candy

 

what we need: 

total original  pieces of candy for Aliya

 

 

Let's say Aliyah has c pieces of candy

 

she took ten pieces for herself which means we can write this as c-10

she then divided this amount between her 4 children (c-10)/4

each child received 2 pieces that means (c-10)/4 =2

 

Now that we have our Algebraic equation we must use algebra to solve for our variable, which is c. Remember when you are solving an algebra equation you must do the same operation in both sides. You will also more or less do PEMDAS backwards. This means you start with addition/subtraction, then you move to multiplication/division, then you deal with exponents, and finally parentheses. 

 

We do not have any addition or subtraction in this problem so we will start with multiplication.

 

(c-10)/4 =2    Multiply both sides by 4 which will cancel out the 4 on the left

 

(c-10) =8 Next we can deal with the parenthesis. Let's add 10 to both sides

 

c = 8 + 10

 

c= 18  So, Aliyah started with 18 pieces of candy.

 

 

We can also check our work by working backward through the problem.

4 children each got 2 pieces of candy

Multiply four times 2

4 x2 =8

 

Aliyah took 10 pieces of candy

Add 10

 

8 +10 = 18   

 

 

Answer 2

Let x = the number of piece she started with

 

 

If she took 10 piece for herself, then the expression we can represent for this part is (x - 10).

 

From there, she divided the rest evenly among her children.  Since she has 4 kids in which each gets 2 pieces, we end up with

 

(x - 10) / 4 = 2

 

 

We solve for x from this equation.

 

Multiply both sides of the equation by 4.

 

x - 10 = 8

 

 

Add 10 to both sides of the equation.

 

x = 18

 

 

 

Answer 3

Hi Justin, 

First, we can make sense of our word problem by grouping the information into a chart: 

Person                  Pieces of Candy 

Aliyah                         10

Child One                     2

Child Two                     2

Child Three                   2

Child Four                     2

Next, we create an equation to find the total amount of candy with which she had started:

10+2+2+2+2=Total Amount of Candy

10+8=Total Amount of Candy

18=Total Amount of Candy

∴Aliyah started with 18 pieces of candy.

Best, 

Star