All Operations in the Order of Operations: Worded problems

To solve this problem, we need to calculate the total number of lollipops currently in the shop.

1. Begin with the initial number of lollipops.
Initially, there are 50 lollipops in the shop.

2. Calculate the additional lollipops received from the delivery.
There are two sets of boxes delivered:

• The first set contains 9 boxes, each having 18 lollipops. Therefore, the total number of lollipops from this set is calculated as: $9 \times 18$.
• The second set includes 6 boxes, each with 14 lollipops. Thus, the total number from this set is: $6 \times 14$.

We will convert the question into an exercise with which we are familiar:

$\left(5\times 13-30\right)+\left(9\times 2-10\right)$

First, we will solve everything that is in the parentheses, starting with the multiplication and division from left to right:

$\left(65-30\right)+\left(18-10\right)$

Then the addition and subtraction operations that are in the parentheses:

$35+8$

Finally, we perform the operations outside of the parentheses:

$35+8=43$

To calculate the average number of apples in each box, we need to find the total number of apples in all the boxes and then divide by the number of boxes.

• First, determine the total number of apples across all boxes. We have:
  $22 + 24 + 14$ apples.
  
  The sum of apples in each box is:
  $22 + 24 + 14 = 60$ apples.



• Next, we find the average by dividing the total number of apples by the number of boxes. There are 3 boxes:
  $\frac{60}{3}$.



• Perform the division:
  $\frac{60}{3} = 20$.

To solve this problem, we need to set up a system of equations based on the information given. We can start by assigning variables to represent the ages of the mother and daughter:
$M$ for the mother's age, and $D$ for the daughter's age.

From the problem statement, we know the following:

• The mother is 25 years older than her daughter: $M = D + 25$.
• The sum of their ages is 40: $M + D = 40$.

We can substitute the first equation into the second equation to solve for $D$:

$(D + 25) + D = 40$

This simplifies to:

$2D + 25 = 40$

Subtract 25 from both sides to isolate the term with $D$:

$2D + 25 - 25 = 40 - 25$

Which is:

$2D = 15$

Now, divide both sides by 2 to solve for $D$:

$D = \frac{15}{2}$

Thus, the daughter's age is $7.5$ years old.

This solution checks out as it satisfies both given conditions in the problem statement.

Since every pair of opposite sides in a rectangle are equal, we know that:

$AB=CD=x+2$

$AD=BC=x$

We can then create the following equation based on the given data:

$30=x+x+2+x+x+2$

$30=4x+4$

$30-4=4x$

$26=4x$

$x=6.5$