For a party, Mary has to bake 5 cakes, 3 pies, and 4 trays of cookies. One cake requires 2.5 cups of flour, one pie requires 1.25 cups of flour, and one tray of cookies needs 0.75 cups of flour. How much flour in all does Mary need to do the baking for the party?

I said 19.25 cups is that correct?

Calculate using expanded notation.
33 + 18=

Use lattice multiplication to find the product.
52 × 67

The product of two numbers is 50. If you divide the larger number by the smaller number you get 2. What are the numbers?

To find the total amount of flour needed for the baking, you need to calculate the amount of flour needed for each item separately and then add them together.

For the cakes:
Number of cakes = 5
Flour per cake = 2.5 cups
Total flour for cakes = 5 * 2.5 = 12.5 cups

For the pies:
Number of pies = 3
Flour per pie = 1.25 cups
Total flour for pies = 3 * 1.25 = 3.75 cups

For the trays of cookies:
Number of trays = 4
Flour per tray = 0.75 cups
Total flour for trays of cookies = 4 * 0.75 = 3 cups

Now, add the total flour needed for each item:
12.5 cups (cakes) + 3.75 cups (pies) + 3 cups (trays of cookies) = 19.25 cups

Therefore, Mary needs 19.25 cups of flour for the baking.

For the calculation using expanded notation:
33 + 18 = 30 + 3 + 10 + 8 = 30 + 10 + 3 + 8 = 40 + 11 = 51

So, 33 + 18 equals 51.

For the lattice multiplication:
67
x 52
-------
134
+ 0
-------
3374

So, 52 multiplied by 67 equals 3,374.

Let's assume the larger number is x and the smaller number is y. According to the given information, we can set up the following equations:
x * y = 50
x / y = 2

Solving these equations simultaneously will give us the values of x and y.

From the second equation, we can rearrange it to get x = 2y.

Substituting this value of x into the first equation:
2y * y = 50
2y^2 = 50
y^2 = 25
y = √25
y = 5

Substituting the value of y (5) back into the equation x = 2y:
x = 2 * 5
x = 10

So, the numbers are x = 10 and y = 5.

To find out how much flour Mary needs in total, we need to calculate the sum of the amount of flour required for each item separately.

First, let's calculate the amount of flour required for the cakes. Since one cake requires 2.5 cups of flour and Mary needs to bake 5 cakes, we multiply 2.5 by 5:

2.5 cups/cake * 5 cakes = 12.5 cups of flour for the cakes.

Next, let's calculate the amount of flour required for the pies. Since one pie requires 1.25 cups of flour and Mary needs to bake 3 pies, we multiply 1.25 by 3:

1.25 cups/pie * 3 pies = 3.75 cups of flour for the pies.

Finally, let's calculate the amount of flour required for the trays of cookies. Since one tray of cookies requires 0.75 cups of flour and Mary needs to bake 4 trays of cookies, we multiply 0.75 by 4:

0.75 cups/tray * 4 trays = 3 cups of flour for the trays of cookies.

Now, add up the amounts of flour needed for each item:

12.5 cups (cakes) + 3.75 cups (pies) + 3 cups (cookies) = 19.25 cups.

So, your answer of 19.25 cups for the total amount of flour Mary needs to bake for the party is correct.

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To calculate 33 + 18 using expanded notation, we can break down each number into the sum of its place values:

33 = 30 + 3
18 = 10 + 8

Then, add up the corresponding place values:

30 + 10 = 40
3 + 8 = 11

Finally, add the results together:

40 + 11 = 51

Therefore, the sum of 33 + 18 using expanded notation is 51.

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To find the product of 52 × 67 using lattice multiplication, follow these steps:

1. Draw a lattice or grid with two horizontal lines and two vertical lines, dividing it into four sections.
2. Place the two numbers (52 and 67) along the top and right edges of the grid.
3. Multiply each digit in the top row by each digit in the right column, and write the partial products diagonally in their corresponding sections.
4. Sum up the partial products diagonally to find the final product.

Here is the step-by-step calculation for 52 × 67:

| 5 | 2 |
---|----|----|
6 | 30 | 12 |
7 | 35 | 14 |

Start from the bottom right corner and work diagonally toward the top left corner, adding the numbers as you go:

14 + 12 + 35 + 30 = 91

Therefore, 52 × 67 equals 91.

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Let's solve the problem of finding two numbers given that their product is 50 and the larger number divided by the smaller number equals 2.

Let's assume the smaller number is x, and the larger number is 2x (since the larger number is twice the size of the smaller number).

We know that their product is 50, so we can set up an equation:

x * 2x = 50

Simplifying the equation:

2x^2 = 50

Divide both sides of the equation by 2 to isolate x^2:

x^2 = 25

Taking the square root of both sides:

x = ±√25

This gives us two possible solutions for x: x = 5 and x = -5.

Since the problem states that we are looking for positive numbers, we can discard the negative solution.

Therefore, the two numbers are 5 and 10, with the smaller number being 5 and the larger number being twice that, which is 10.