Mixed ReviewJorge bought a crate of floor ties
for $95.94. The crate had 6 boxes of floor tiles. Each box
1. contained 20 floor tiles. Write and solve an
equation to determine the cost per box, b. Then
write and solve a second equation to determine the cost per tile, t, to the nearest cent.
2. A convenience store sells two brands of orange juice. Brand A contains 8 fluid ounces and
costs $1.28. Brand B contains 12 fluid ounces and costs $1.68. What is the difference in cost, in
dollars, per fluid ounce between the two brands of juice?
Answers
Answers with working:
1.
Cost of a crate of floor tiles = $95.94
The crate has 6 boxes of floor tiles. This means 6 boxes of tiles cost $95.94
Now each box has 20 floor tiles.
So, total tiles in a box are : tiles
Now, cost of 6 boxes = $95.94
So, cost of 1 box (b) = = $15.99
20 tiles cost $15.99
Hence, 1 tile (t) will cost = = $0.799 ≈ $0.80
2.
Brand A contains 8 fluid ounces and costs $1.28.
Cost of per fluid ounce = = $0.16
Brand B contains 12 fluid ounces and costs $1.68.
Cost of per ounce = = $0.14
Difference between both the per ounce costs = = $0.02
= $15.99
t = $15.99 / 20
= $0.80
2. A: $1.28 / 8 = $0.16 per oz
B: $1.68 / 12 = $0.14 per oz
Difference: $0.02 per oz
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Answers
Answers
First, let's see if they can cancel out. Nope. 3 and 8 have no common factors, and neither do 4 and 9.
When you're multiplying fractions together, you can switch out the numerators and denominators (if it helps you visualize things more easily. You won't need to do this step with some practice).
3/8 × 4/9 =
3/9 × 4/8 =
Now three 3 and 9 both have a common factor of 3. Divide them both by that common factor, top and bottom.
3/9 × 4/8 = //Comment: 3 ÷ 3 = 1, 9 ÷ 3 = 3.
1/3 × 4/8 =
4 and 8 likewise have a common factor, but of 4. Divide them both by that common factor. Remember, what you divide or multiply from the top, must also be done with the bottom and vice version. This way it will cancel out.
1/3 × 4/8 = //Comment: 4 ÷ 4 = 1, 8 ÷ 4 = 2.
1/3 × 1/2 =
Now multiply the numerators to each other, and the denominators to each other.
1/3 × 1/2 =
(1 × 1)/(3 × 2) =
1/(3 × 2) =
1/6
That is your answer. To check, we can do the opposite operation. In this case, you can divide the answer by either of the two original fractions and you should get the other. That's a little more advanced though, but a quick and easy way to convert from fraction division to fraction multiplication is to invert the fraction and the division sign to a multiplication sign.
1/6 ÷ 3/8 = 4/9 //Comment: Invert fraction and division sign.
1/6 × 8/3 = 4/9 //Can we cancel out any thing?
1/3 × 8/6 = 4/9
8 and 6 have a common factor of 2. Divide both by that factor.
1/3 × 8/6 = 4/9 //Comment: 8 ÷ 2 = 4, 6 ÷ 2 = 3
1/3 × 4/3 = 4/9
Multiply the numerators together and the denominators together.
1/3 × 4/3 = 4/9
(1 × 4)/(3 × 3) = 4/9
4/(3 × 3) = 4/9
4/9 = 4/9
4/9 = 4/9 which is true. If you like, try it out with 1/6 ÷ 4/9 :)
Answers
Answer:
Step-by-step explanation:
Let
x -----> Kevin’s savings accounts amount at the beginning of the month
Remember that
we know that
The amount in Kevin’s account at the end of the month is equal at the amount at the beginning of the month multiplied by 1.04
so
B. 1,506 in²
C. 1,560 in²
Answers
The surface area of the composite shape is 1560 square inches
Step-by-step explanation:
The surface area of the top cardboard is,
SA = 5 x area of each side
Because one side is attached with another cardboard box . So while finding the area only 5 sides are calculated.
SA = 5 ( 10 x 10)
= 500 square inches
The surface area of the rectangular prism cardboard,
Given that,
l = 20 in
w =15 in
h = 8 in
A = 2(lw + wh + hl) - 100
We are subtracting 100 because it is the area of one side of the square cardboard box on top of the rectangular prism box .
A = 2(300 + 120 + 160) - 100
= 2(580) - 100
= 1160-100
= 1060 square inches
Total surface area = SA + A
= 500 + 1060
= 1560 square inches
The surface area of composite shape is 1760 square inches, if two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in and the bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step-by-step explanation:
The given is,
The top box is a cube with sides of 10 in
The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step:1
Surface area of composite figure = Surface area of cube +
Surface area of rectangular prism
Step:2
Formula for surface area of cube,
( Only 5 sides area considered )
Where, a - Side of cube
From given, a = 10 inches
From the surface area equation,
= (5)(100)
= 500
Surface area of cube = 500 square inches
Step:3
Formula surface area of rectangular prism,
Where, w - Width
l - Length
h - Height
From the given values.
w = 15 inches
l = 20 inches
h = 8 inches
Surface area equation becomes,
= 2 ( 300 + 160 + 120 )-100
= 2 (580)-100
Surface area of rectangular prism = 1060 square inches
From the step 1,
Surface area of composite shape = 500+1060
= 1560 square inches
Result:
The surface area of composite shape is 1560 square inches.
Answers
30/24 = 18/x
x stands for how wide in cm.
30/24 = 18/x
Cross multiply
30*x = 30x
24*18 = 432
432 = 30x
30x/30 = 432/30
x= 14.4
Answer: The width should be 14.40 cm wide.
18 - 6 = 12
12 cm wide
Answers
Answer:
There are a maximum of eight 3's inside 26
Step-by-step explanation:
To find how many times does 3 go into 26, we just have to find a number which multiplied with 3 is near 26.
We have 3 x 8 = 24, which the nearest number possible we can have from 3.
Therefore, there are a maximum of eight 3's inside 26, and a remaining of 2.
3 goes into 26 eight times with a remainder of 2.
Given that we need to determine that how many times does 3 go into 26
To determine how many times 3 goes into 26, we can divide 26 by 3 using long division.
Here's how it works:
8
------------
3 | 26
-24
---
2
We start by dividing the leftmost digit of 26, which is 2, by 3. Since 3 cannot evenly divide into 2, we bring down the next digit, which is 6, to create the number 26.
Now, we divide 26 by 3. 3 can go into 26 eight times (8 x 3 = 24). We subtract 24 from 26, which leaves us with a remainder of 2.
This means that 3 goes into 26 eight times with a remainder of 2. In other words, you can evenly divide 26 by 3 eight times, and there will be a remainder of 2 left over.
Therefore, 3 goes into 26 eight times with a remainder of 2.
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