Solving an Equation by Multiplication/ Division: Solving an equation with fractions

To solve the equation $\frac{x+2}{3}=\frac{4}{5}$, we can follow the method of cross-multiplication:

• Step 1: Cross-multiply to eliminate the fractions, giving us:

$(x + 2) \cdot 5 = 4 \cdot 3$

• Step 2: Simplify both sides of the equation:

$5(x + 2) = 12$

• Step 3: Distribute the 5 on the left side:

$5x + 10 = 12$

• Step 4: Subtract 10 from both sides to isolate the term with $x$:

$5x = 2$

• Step 5: Divide both sides by 5 to solve for $x$:

$x = \frac{2}{5}$

Therefore, the solution to the equation is $\frac{2}{5}$.

To solve $\frac{x-5}{7} = \frac{2}{11}$, we will use cross-multiplication:

• Step 1: Cross-multiply the equation: $(x-5) \times 11 = 7 \times 2$.
• Step 2: Simplify both sides: $11(x - 5) = 14$.
• Step 3: Distribute the 11 on the left side: $11x - 55 = 14$.
• Step 4: Add 55 to both sides to isolate the $11x$ term: $11x = 14 + 55$.
• Step 5: Calculate the right side: $11x = 69$.
• Step 6: Divide both sides by 11 to solve for $x$: $x = \frac{69}{11}$.

Therefore, the solution to the problem is $x = \frac{69}{11}$, which matches the first answer choice provided.

To solve this problem, we'll use a step-by-step approach:

Step 1: Set up the equation based on the problem statement.
The total cost Lionel pays is given by the formula:

$4.5x = 45$

Here, $x$ is the number of packs Lionel buys, and $4.5 is the cost per pack.

Step 2: Solve for $x$.
To find $x$, divide both sides of the equation by 4.5:

$x = \frac{45}{4.5}$

Step 3: Perform the division.
Carrying out the division,

$x = \frac{45}{4.5} = 10$

Therefore, Lionel buys $x = 10$ packs of paper.

To solve for the price per kg of cucumbers, follow these steps:

• Step 1: Determine the total cost of tomatoes.
  Given that the cost of tomatoes is $2.8 per kg, and Maggie buys 2 kg, the cost of tomatoes is calculated as:
  $2 \, \text{kg} \times 2.8 \, \text{dollars/kg} = 5.6 \, \text{dollars}$.

• Step 2: Write the equation for total cost.
  The total cost for tomatoes and cucumbers combined is given as $7.1. Let $x$ represent the cost per kg of cucumbers. The equation representing the total cost is:
  $5.6 + 0.6x = 7.1$.

• Step 3: Solve the equation for $x$.
  Subtract the cost of tomatoes from both sides of the equation to find the cost of cucumbers:
  $0.6x = 7.1 - 5.6$.
  Simplifying the right side gives:
  $0.6x = 1.5$.

• Step 4: Isolate $x$ by dividing both sides by 0.6:
  $x = \frac{1.5}{0.6}$.
  Simplify the division to find $x$:
  $x = 2.5$.

Therefore, the value per kg of cucumbers is $x = 2.5$ dollars.