Ellie and Morgan go to the movie theater and purchase refreshments for their friends. Ellie spends a total of $36.50 on 7 bags o
f popcorn and 2 drinks. Morgan spends a total of $155.50 on 9 bags of popcorn and 14 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
1 answer:
Equations are set up by who bought what, and the P stands for popcorn and the D for drinks
1) multiply first equation by -7 so that the Ds are able to cancel out
2) place the second equation right under the first and add the 9p to -49p and so on
3)divide by -40 on both sides and the answer for p is $2.50
4) plug p into the equation
5)multiply 7 and 2.5 and subtract 17.5 on both sides
6) divide on both sides by 2
The amount for drinks is $8
1) multiply first equation by -7 so that the Ds are able to cancel out
2) place the second equation right under the first and add the 9p to -49p and so on
3)divide by -40 on both sides and the answer for p is $2.50
4) plug p into the equation
5)multiply 7 and 2.5 and subtract 17.5 on both sides
6) divide on both sides by 2
The amount for drinks is $8
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Answer: x = -4 ; Angle = 60°
Concept:
The given figure is a triangle with 3 arc signs on each angle. This <u>arc sign </u>stands for the corresponding angles are congruent, which in this question, it shows that all three angles are congruent. Sometimes, if the figure has multiple angles and there are different groupings of congruent angles, then we use different numbers of arcs or symbols.
Solve:
<u>Given information</u>
An angle = 3x + 72
Total measure of angles = 180 (triangle angle sum theorem)
Total number of congruent angles = 3
<u>Given expression</u>
Total measure = Total number of congruent angles × An angle measure
<u>Substitute values into the expression</u>
180 = 3 (3x + 72)
<u>Divide 3 on both sides</u>
180 / 3 = 3 (3x + 72) / 3
60 = 3x + 72
<u>Subtract 72 on both sides</u>
60 - 72 = 3x + 72 - 72
-12 = 3x
<u>Divide 3 on both sides</u>
-12 / 3 = 3x / 3
<u />
<u>Find the angle measure</u>
3x + 72 = 3 (-4) + 72 =
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Answer:
A.
Step-by-step explanation:
Surface area of the original cone
When, radius is quadrupled and slant height is reduced to one sixth
Plug the above values of r and in equation (1), new surface area becomes: