Lesson 5

An alcohol solution was made by mixing 2 gal. of a 90% alcohol solution and 1 gal. of a 45% alcohol solution. What is the concentration of the mixture?

Kim wants to make a 12% acid solution. She has already poured 1 fl. oz. of a 40% acid solution into a beaker. How many fl. oz. of a 5% acid solution must she add to this to create the desired mixture?

One line passes   $\left(2,8\right)$  and  $\left(-3,13\right)$  . A second line passes through the points    $\left(1,3\right)$  and  $\left(5,7\right)$ . At what point do the two lines intersect?

Daniel and Natalie are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and strawberry cheesecakes. Daniel sold 7 New York style cheesecakes and 14 strawberry cheesecakes for a total of $210. Natalie sold 14 New York style cheesecakes and 11 strawberry cheesecakes for a total of $216. Find the cost each of one New York style cheesecake and one strawberry cheesecake.

(New York style cheesecake, strawberry cheesecake)

Taylor’s aquarium has six times as many fish as frogs. If a quarter of her frogs plus a third of her fish equals nine, how many frogs does Taylor have in her tank?

A boat traveled 189 miles downstream and back. The trip downstream took 9 hours. The trip back took 27 hours. Find the speed of the boat in still water and the speed of the current.

(boat, current)

A fishing boat left Port 59 and traveled west. An aircraft carrier left two hours later traveling at 25 mph in an effort to catch up to the fishing boat. After traveling for three hours the aircraft carrier finally caught up. Find the fishing boat's average speed.

Solve each system by substitution. Write your answers:
(x,y) or x,y
I = infinite
NS = no solution

Solve the equation. Write both answers: smaller number, larger number

ex. (-1,7) or -1,7

Solve the equation for x. If x equals a number, write the number, if not:
I = infinite
NS = no solution

Simplify. Your answer should only contain positive exponents. Use ^ for exponents. Write answers in alphabetical order.