Kara spent a total of $8.75 on 5 pens and a packet of paper. If the packet of paper cost $3.95, how much did each pen cost?
Choices:
Each pen cost $0.96
Each pen cost $1.20.
Each pen cost $1.75
Each pen cost $4.80.
2. A family purchased t-shirts for a family reunioin. They paid a total of $154 for 8 adult shirts and 15 child shirts. The price of a child shirt was three-fourths the price of an adult shirt. How much was the price of an adult shirt?
Choices:
An adult shirt cost $12.
An adult shirt cost $8.
An adult shirt cost $10.67.
An adult shirt cost $6.70.
3. The three angles in the triangle shown below are labeled M, N, and P. The sum of the interior angle measures of a triangle is 180 degrees.
Angle N is n degrees.
Angle P is two times the measure of angle N.
Angle M is 54 degrees.
Find the value of n.
CHoices:
n=60
n=78
n=42
n=63
I gave you the equations that you need to solve to answer the questions.
It should have been obvious what the variables represented.
1. To find out how much each pen cost, we need to subtract the cost of the packet of paper from the total cost.
Total cost - Cost of packet of paper = Cost of pens
$8.75 - $3.95 = $4.80
Therefore, each pen cost $4.80.
So the correct choice is: Each pen cost $4.80.
2. Let's assume the price of an adult shirt is x dollars.
Price of a child shirt = (3/4) * Price of an adult shirt = (3/4) * x
Total cost = (Price of adult shirts * Number of adult shirts) + (Price of child shirts * Number of child shirts)
$154 = (x * 8) + ((3/4) * x * 15)
Simplifying the equation, we have:
154 = 8x + (45/4)x
Multiply through by 4 to remove the fraction:
616 = 32x + 45x
Combine like terms:
616 = 77x
Divide both sides by 77:
x = 8
Therefore, the price of an adult shirt is $8.
So the correct choice is: An adult shirt cost $8.
3. We are given the measure of angle M as 54 degrees.
Angle P is two times the measure of angle N:
Angle P = 2n
The sum of the angles in a triangle is 180 degrees:
Angle M + Angle N + Angle P = 180
Substituting the given values and expressing Angle N and Angle P in terms of n:
54 + n + 2n = 180
Collect like terms:
3n + 54 = 180
Subtract 54 from both sides:
3n = 126
Divide both sides by 3:
n = 42
Therefore, the value of n is 42.
So the correct choice is: n = 42.
1. To find out how much each pen cost, we need to subtract the cost of the packet of paper from the total cost. So, the total cost of the pens is $8.75 - $3.95 = $4.80. Since there are 5 pens, we divide the total cost by 5 to find out the cost of each pen. Therefore, each pen cost $4.80 / 5 = $0.96.
Therefore, the correct choice is: Each pen cost $0.96.
2. Let's first assume the price of an adult shirt as "x". According to the given information, the price of a child shirt is three-fourths the price of an adult shirt. So, the price of a child shirt is (3/4)x.
The family purchased 8 adult shirts and 15 child shirts, so we can set up the equation:
8x + 15(3/4)x = $154
Simplifying the equation, we get:
8x + 45/4 x = $154
Multiplying through by 4 to eliminate the fraction, we get:
32x + 45x = $616
Combining like terms, we get:
77x = $616
Dividing both sides of the equation by 77, we get:
x = $616 / 77 = $8
Therefore, the price of an adult shirt is $8.
Therefore, the correct choice is: An adult shirt cost $8.
3. Let's solve for the value of n by using the information given. We know that the sum of the interior angles of a triangle is 180 degrees.
Angle P is two times the measure of angle N, so we can write it as P = 2N.
Angle M is given as 54 degrees.
To find the value of n, we need to find the measure of angle N. We can substitute the values into the equation:
Angle N + Angle P + Angle M = 180 degrees.
n + 2n + 54 = 180
Combining like terms, we get:
3n + 54 = 180
Subtracting 54 from both sides of the equation, we get:
3n = 180 - 54 = 126
Dividing both sides of the equation by 3, we get:
n = 126 / 3 = 42
Therefore, the value of n is 42.
Therefore, the correct choice is: n = 42.