Algebra 1, 2 – systems of equations

Q: 100 people are to be seated at 22 tables. Some tables seat 4 people and some seat 6 people. If no seats are empty, how many tables seating 4 people are there?
 
Answer: 16
Explanation:  Solve the system: x + y = 22; 4x + 6y = 100.  My ‘CRAMER’ program will solve this for you! The number of 4-person tables is the x-value of the solution.
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Algebra 1 – distance

Q: To the nearest tenth, what is the distance between the points (-6,2) and (6,5)?
 
Answer:  12.4 
(Use the distance formula, and round to the nearest tenth.)
My TI-84 Plus program DISTANCE will find this value.
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SAT – Counting and Ordering

Q: Bob has ten different books, but must choose only three to bring along on his vacation. In how many ways can Bob choose three books?
 
Answer: 120
Explanation: This is a combination (not permutation) problem, because the order of the books in Bob’s bag does not matter.  Find the nCr function on your calculator and enter ’10 nCr 3′.  On the TI-84 Plus, nCr is in MATH, PRB, 3.  Or, do this by hand using the formula for nCr.
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Algebra 1, 2 – systems of equations

Two cubes and one pyramid weigh 9 lb. Seven cubes and two pyramids weigh 24 lb. All cubes weigh the same, and all pyramids weigh the same. What is the weight of one pyramid?

 
Answer: 5 lb

Explanation:  Let x be the weight of a cube.  Let y be the weight of a pyramid. 

The first sentence becomes: 2x + y = 9. 

The second sentence is: 7x + 2y = 24. 

Solve this as a system of equations by any method you choose… substitution, elimination, Cramer’s Rule, etc.  Or use my TI-84 Plus program ‘CRAMER’.

x = 2, y = 5

‘y’ is the weight of one pyramid, so the answer is 5.

 

 

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