Math  /  Algebra

Questionof eache Mrs. Singh bought 9 folders and 9 notebooks. The cos expressions and then find Each noteboo \qquad cost \4.Writetwoequivalent4. Write two equivalent \qquad$ Be Precise five friends bought admission a box lunch. The cost of unctreost

Studdy Solution

STEP 1

What is this asking? We need to find two different ways to calculate the total cost of 9 folders and 9 notebooks, knowing the price of each. Watch out! Don't mix up the prices of the folders and notebooks!

STEP 2

1. Calculate the cost of the folders.
2. Calculate the cost of the notebooks.
3. Calculate the total cost using the distributive property.
4. Calculate the total cost by adding the number of items first.

STEP 3

We know Mrs.
Singh bought 99 folders, and each folder costs $2.50\$2.50.
To find the **total cost** of the folders, we **multiply** the number of folders by the cost per folder.
This makes sense, right?
If one folder costs $2.50\$2.50, then two folders cost $2.502\$2.50 \cdot 2, three cost $2.503\$2.50 \cdot 3, and so on!

STEP 4

So, the cost of the folders is 9$2.50=$22.509 \cdot \$2.50 = \$22.50.
Boom!

STEP 5

Now, let's do the same thing for the notebooks.
Mrs. Singh bought 99 notebooks, and each one costs $4\$4.
To get the **total cost** of the notebooks, we **multiply**!

STEP 6

The cost of the notebooks is 9$4=$369 \cdot \$4 = \$36.
Awesome!

STEP 7

One way to find the **total cost** is to **add** the cost of the folders and the cost of the notebooks.
We already calculated those, so let's bring them back!

STEP 8

Total cost = Cost of folders + Cost of notebooks.
So, $22.50+$36=$58.50\$22.50 + \$36 = \$58.50.
Fantastic! This is one way to write the expression: 9$2.50+9$49 \cdot \$2.50 + 9 \cdot \$4.

STEP 9

Since Mrs.
Singh bought the same number of folders and notebooks (99 of each), we can think of it like this: She bought 99 sets of a folder and a notebook.

STEP 10

How much does one set cost?
It's the cost of one folder ($2.50\$2.50) plus the cost of one notebook ($4\$4), which is $2.50+$4=$6.50\$2.50 + \$4 = \$6.50.

STEP 11

Now, since she bought 99 of these sets, the total cost is 9$6.50=$58.509 \cdot \$6.50 = \$58.50.
This is another way to write the expression: 9($2.50+$4)9 \cdot (\$2.50 + \$4).
See how it matches the total cost we calculated before?
Amazing!

STEP 12

The two equivalent expressions are 9$2.50+9$49 \cdot \$2.50 + 9 \cdot \$4 and 9($2.50+$4)9 \cdot (\$2.50 + \$4).
The total cost of the folders and notebooks is $58.50\$58.50.

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