Double digit subtraction with regrouping

Margot has 21 1/2 pounds of flour 8 pounds of butter and 18 1/2 ponds of sugar to make shortbread cookies if she makes 12 batche

adell [148]

Answer:

4 pounds of ingredients are used in each batch.

Step-by-step explanation:

Amount of flour = $21\frac{1}{2}pounds = \frac{43}{2}pounds$

Amount of butter = 8 pounds

Amount of sugar = $18\frac{1}{2}pounds= \frac{37}{2} pounds$

So, the total amount of all ingredients will be: $(\frac{43}{2}+\frac{37}{2}+8)pounds = (\frac{43+37+16}{2}) pounds= \frac{96}{2} pounds = 48 pounds$

Given that, she makes 12 batches of cookies using all the ingredients.

Thus, the amount of ingredients used in each batch $=\frac{48}{12} pounds = 4 pounds$

5 0

3 years ago

Ms. Brack wants to hang a bulletin board with

Eduardwww [97]

Answer:

He needs 8.75 ft² polka dot paper to cover the board.

Step-by-step explanation:

How much polka dot paper she need to cover the board is the area of the board . The is a rectangle with length 3.5 ft long and width of 2.5 ft wide .

The area of the board(rectangle) = length × width

Area = LW

where

L= 3.5 ft

W = 2.5 ft

Area = 3.5 × 2.5

Area = 8.75 ft²

He needs 8.75 ft² polka dot paper to cover the board.

7 0

3 years ago

A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

3 years ago

6 (3x-1)-10x. with work please :)

STatiana [176]

Hey there!
Let's break this expression into two parts:
6(3x-1) and -10x

To solve the first part, we need to use the distributive property which states:
a(b+c) = ab+ac

Applying that to this problem, we have:
6(3x) + 6(-1) =
18x - 6

Now, we can take that -10x and put it right back in:

18x - 6 - 10x

Combine like terms and subtract the 10x from the 18x to get:
8x - 6

Hope this helps!

4 0

3 years ago

Which statement is true about the ranges for the box plots?

agasfer [191]

Answer:

The range of the Morning box plot is the same as the range of the Afternoon box plot.

Step-by-step explanation:

Data provided in the question

Number line = 0 to 16

Morning whiskers range = 3 to 15

Box range = 5 to 12

Line divided = 8

Afternoon whiskers range = 4 to 16

Box range = 8 to 15

Line divided = 14

Based on the above information,

The morning whiskers range difference is

= 12 - 5

= 7

And, the afternoon whiskers range difference is

= 15 - 8

= 7

Therefore the first option is correct

4 0

3 years ago

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