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Systems of Linear Equations

Systems of Linear Equations

Systems of Linear Equations: The Way We Word (Problems) True or False

1. Which system of equations best represents the following situation? 

Brent and Kay work as carpenter's apprentices. On the first day Brent worked for 4 hours and Kay worked for 5 hours, and they hammered in a total of 305 nails. On the second day Brent worked for 3 hours and Kay worked for 7, and they hammered in a total of 349 nails. On the third day, the master carpenter they were working for asked them to stop hammering so many nails into the ground and get back to building the woodshed.


2. An isosceles triangle with sides of lengths x, x, and y has perimeter 14. If each side of the triangle is extended by 3, the perimeter of the new triangle is 23. What are the side lengths of the original triangle? -> Infinitely many triangles fit this description.
3. A rectangle has perimeter 50 cm. A new rectangle is formed whose width is the same as the original rectangle, and whose length is obtained by doubling the length of the original rectangle and adding 3. The perimeter of the new rectangle is 86 cm. What are the dimensions of the original rectangle? -> 10 cm x 15 cm
4. The sum of two numbers is 36. Their difference is 8. What is the larger of the two numbers? -> 31
5. The sum of y and twice x is 41. The difference of half of x and y is -11. What is x? -> 12
6. A special room in a local zoo has a combined total of fifty-three three-legged whatsits and four-legged whosits. Honestly, we question the integrity of this "zoo." The special room contains 191 legs. How many whatsits are in the room? -> 32
7. Ben has a handful of dimes and quarters worth $6.70. After giving away 3 dimes and half the quarters, he is left with $3.90. He is also left with the feeling that he may be able to benefit from the services of a financial advisor. How many dimes did Ben start with? -> 14
8. Shoshana has forty coins. One quarter of these coins are quarters, and the rest are a combination of dimes and nickels. If Shoshana has $4.45, how many nickels does she have? -> 47
9. Aida and Malika went on a road trip. Aida always drives one speed, and Malika always drives one speed. On the first day of the trip Aida drove for 2 hours and Malkia drove for 4. On the second day Aida and Malika each drove for 3 hours. The first day they went 354 miles and the second day they went 357 miles. Man...they must be stopping to take in all the sights. Hope they're not in a hurry. 

How many miles did Aida drive on the second day?

-> 183

10. Betty wants to mix 70% dark chocolate and 20% milk chocolate to get one pound (16 oz) of 40% chocolate. How many ounces of dark chocolate does she need to start with? -> 2.5