Solving Equations by using Addition/ Subtraction: Worded problems

To solve this problem, we'll follow these steps:

• Step 1: Define the variable for Camila's balls.
• Step 2: Set up an equation to sum their findings.
• Step 3: Solve the equation for Camila's ball count.

Now, let's work through each step:

Step 1: Let $x$ be the number of balls Camila finds.
Step 2: According to the problem, David finds 8 more balls than Camila, so he finds $x + 8$ balls.
Therefore, the equation representing the total number of balls is:
$x + (x + 8) = 16$.

Step 3: Simplify and solve for $x$:

$x + x + 8 = 16$

Combine like terms:

$2x + 8 = 16$

Subtract 8 from both sides:

$2x = 8$

Divide both sides by 2:

$x = 4$

Therefore, the number of balls found by Camila is $4$.

To solve this problem, let's define the variables and set up the equation:

• Let Ivana's age be $x$.
• Then, Luciana's age is $3x$, since her age is three times Ivana's age.
• Hector, being 10 years younger than Luciana, would be $3x - 10$.

We know the sum of their ages is 32, so we set up the equation:

$x + 3x + (3x - 10) = 32$

Simplify the equation:

$x + 3x + 3x - 10 = 32$

$7x - 10 = 32$

Next, solve for $x$:

Add 10 to both sides:

$7x = 42$

Divide both sides by 7:

$x = 6$

Now that we know Ivana is 6 years old, we can find Hector's age:

Hector's age = $3x - 10 = 3(6) - 10 = 18 - 10 = 8$

Therefore, Hector is 8 years old.

To solve this problem, we'll follow these steps:

• Step 1: Identify the prices of apples and cucumbers in terms of a variable.
• Step 2: Set up the equation for the total cost.
• Step 3: Solve the equation to find the price of cucumbers.

Now, let's work through each step:

Step 1: Let the price per kg of cucumbers be $c$ dollars. Thus, the price per kg of apples is $c + 8$ dollars.

Step 2: Express the total cost of the items:

For 3 kg of apples: $3 \times (c + 8)$
For 5 kg of cucumbers: $5 \times c$

These add up to give the total cost:

$3(c + 8) + 5c = 48$

Step 3: Solve the equation.

Expand the equation:

$3c + 24 + 5c = 48$

Combine like terms:

$8c + 24 = 48$

Subtract 24 from both sides:

$8c = 24$

Divide by 8:

$c = 3$

Therefore, the price of 1 kg of cucumbers is $3$ dollars.

We will identify the price of the notebook with x and since the price of the pen is 2 times greater we will mark the price of the pen with 2x

The resulting equation is 4 times the price of a pen plus 9 times the price of a notebook = 51

Now we replace and obtain the following equation:

\( 4\times2x+9\times x=51

According to the rules of the order of arithmetic operations, multiplication and division operations precede addition and subtraction, therefore we will first solve the two multiplication exercises and then add them up:

$(4\times2x)+(9\times x)=51$

$(4\times2x)=8x$

$(9\times x)=9x$

$8x+9x=17x$

Now the obtained equation is: $17x=51$

We divide both sides by 17 and find x

$x=\frac{51}{17}=3$

As we discovered that x is equal to 3, we will place it accordingly and find out the price of a pen:$2\times x=2\times3=6$

To solve this problem, we'll perform the following steps:

• Step 1: Define $x$ as the number of pages in file B.
• Step 2: Express the number of pages in file A as $8x$.
• Step 3: Establish the equation based on the problem statement: $8x = x + 35$.
• Step 4: Solve the equation for $x$.
• Step 5: Calculate the number of pages in file A using the relationship $8x$.

Now, let's solve it step by step:
Step 1: Let $x$ represent the number of pages in file B.

Step 2: The number of pages in file A is 8 times that of file B, so it is $8x$.

Step 3: Form the equation based on adding 35 pages to file B: $8x = x + 35$.

Step 4: Solve for $x$:
Subtract $x$ from both sides to consolidate terms:
$8x - x = x + 35 - x$
This simplifies to $7x = 35$.

Step 5: Solve for $x$ by dividing both sides by 7:
$x = \frac{35}{7} = 5$.

Now, substitute back to find the number of pages in file A:
The number of pages in file A is $8x = 8 \times 5 = 40$.

Therefore, the number of pages in file A is $40$.

In the first step, we will try to use variables to change the exercise from verbal to algebraic.

Let's start with the third daughter and define her age as X.

The second daughter, as written, is 5 times older than her, so we will define her age as 5X.

The first daughter is 2 times older than the second daughter, so we will define her age as 2*5X, that is, 10X.

Now let's look at the other piece of information: it is known that if we increase the age of the third daughter by 12 years, then she will be the same age as the second sister.

So we will write X+12 (the third daughter plus another 12 years)

=

5X (age of the second daughter)

X + 12 = 5X

Once we have an equation, we can solve it. First, we'll move the sections:

5X-X=12

4X=12

We divide by 4:

X=3

But this is not the solution!

Remember, we were asked for the age of the first daughter, which is 10X

We replace the X we found:

10*3 = 30

This is the solution!