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Answer: 12 dimes and 5 quarters
Step-by-step explanation: Let's start this problem by setting up a chart so we can organize our information that we're given in this problem.
Down the left side, we'll have our different types of coins. In this case dimes and quarters. Across the top we'll have our formula which is shown below.
Number of coins · value of each coin = total value
Now let's fill out our chart.
For number of dimes and quarters, we know that mark has a total of 17 dimes and quarters but we don't know how many of each he has. In fact, that's what the problem is asking.
So if we represent our number of dimes as <em>x</em>, we can call our number of quarters <em>17 - x</em>.
The value of each dime is 10¢ and the value of each quarter is 25¢.
Our total value based on our formula is going to come from the first column times the second column. So the total value of our dimes is <em>x times 10</em> or <em>10x </em>and the total value of our quarters is <em>17 - x times 25</em> or <em>25 (17 - x)</em>.
Our goal in this problem will be to find <em>x </em>because <em>x</em> represents our number of dimes and the problem asks how many dimes does he have. If we know the number of dimes, we can easily find the number of dimes and we'll have our answer. However, we need an equation in order to find <em>x</em>.
It's important to understand that he information in this equation will always come from the last column of your chart, the total value column. So what do we know about the total value of our dimes and the total value of our quarters?
Well we know that the total value of all of our coins is $2.45. So if we add the total value of our dimes + the total value of our quarters, that should equal $2.45. So below the chart I added an additional box and I put 245 in it. Notice that I wrote 245 in terms of cents because our value of dimes and value of quarters is also written in terms of cents and we need to be constient.
So here's our equation.
10x + 25 (17 - x) = 245.
If we solve this, we get <em>x = 12</em>.
Going back up into our chart, remember that <em>x</em> represents our number of dimes so Mark has 12 dimes. To get his number of quarters, we take 17 - x which is 17 - 12 or 5 quarters and that's our answer.
I have also attached the chart that I have made below.
Answer:
D. 26
Step-by-step explanation:
Answer:
QUESTION 2:
The area of the polygon is 21.5 units²
QUESTION 3:
The area of the combined figure is 12 + 18.25·π units²
QUESTION 4:
The area of the figure is 40 units²
QUESTION 5
The area of the compost shape is 40 in.²
Step-by-step explanation:
QUESTION 2.
The area of the polygon is given as follows;
The area of two triangles + The area of trapezoid
1/2×6×3 + 1/2×3×4 + 1/2×(6 + 7) = 21.5 units²
QUESTION 3
The diameter of the semicircle, 'd', is given as follows;
d = √(8² + 3²) = √73
The area of the semicircle = π·d²/4 = π·73/4 = 18.25·π unit²
The area of the right triangle beside the semicircle is given as follows;
1/2 × 8 × 3 = 12 unit²
The area of the combined figure = The area of the semicircle + The area of the right triangle
∴ The area of the combined figure = 12 + 18.25·π units²
QUESTION 4:
The dimensions of the parallelogram are;
Width, W = √(4² + 1²) = √(17)
Length, L = √(8² + 2²) = √(68)
The area of the parallelogram, = W × L = √(17) × √(68) = √(17 × 68) = 34
The area of the parallelogram, = 34 units²
The length of a parallel side, 'A', of the parallelogram is A = 6
The height of the parallelogram, is h = 1
The area of the parallelogram is A = B·h = 6 × 1 = 6 units²
The area of the figure is the sum of the area of the rectangle and the area of the parallelogram
Therefore, we have;
The area of the figure = 34 units² + 6 units² = 40 units²
QUESTION 5
The composite shape consists of a triangle and a rectangle
Therefore, we have;
The area of the rectangle = 5 in. × 7 in. = 35 in.²
The area of the triangle = 1/2 × 2 in. × 5 in. = 5 in.²
The area of the compost shape = The area of the rectangle + The area of the triangle
∴ The area of the compost shape = 35 in.² + 5 in.² = 40 in.²
The area of the compost shape = 40 in.².