First up: number 2.
The system of equations you should set up is this:
Let x represent ounces of cider from tub A
Let y represent ounces of cider from tub B
x + y = 64
.12x + .55y = .20(64)
Does this make sense?
2. Tub A contains 12% apple cider.
Tub B contains 55% apple cider.
How many ounces of cider from each tub
must be gotten to make a 64 ounce drink that
is 20% apple cider?
3. Mary is running to school. She leaves home at
7:00 AM trotting at a speed of 12 mph.
Her little lamb leaves home at 7:15 AM
running after her at a speed of 17 mph.
What time of day will the lamb catch Mary?
Round your answer to the nearest minute.
(Example: 10:27 AM)
4. Granny needs 3 gallons of 15% vinegar for
her pickles. Bud went to the store and bought
2 gallons of 50% vinegar. Granny asks:
How much pure spring water must I mix with
some of that 50% stuff to get my canner
filled with 3 gallons of 15% solution?
5. Use the formulae:
Given: distance =16t^2 for a falling object,
And the fact that distance=1100 *t, where the speed of sound is 1100ft/sec in air.
If you drop a rock into a deep dark well and note that it takes 7 seconds to hear a splash after you drop the rock, how deep is the well? Hint: it takes some time for the rock to fall and then the remainder of the time for sound to travel back up the well for you to hear the splash. You will need the Quadratic formula to solve this one.
7. Calculate the Medical Dosage.
Given that a saline medicine bottle contains 5 milligrams
of Tylenol for each 9 ml of saline
solution in which it is dissolved.
Grandma Wilson, who weighs 188 pounds needs
25 milligrams of Tylenol per 50 kilograms of body
weight for an I.V. How many ml of saline must she be administered?
Note: 1kilogram=2.2pounds
8. I have a collection of nickels, dimes, and quarters
in a money bag worth $7.95. If the number of
quarters is one more than the number of nickels
and the number of dimes is five more than the number
of nickels, find the number of each type of coin.
# Nickels ________
# Dimes_________¬
# Quarters________
9. Freezing weather is coming!
The radiator in my 450 John Deere track loader
is full with 18 quarts of fluid that is 15% antifreeze.
Question: How much must I drain out into a disposable container,
Then retighten drain plug, and pour back 100% pure
antifreeze into radiator to make 18 quarts of 40%
antifreeze.
I would use substitution.
x + y = 64
.12x + .55y = .20(64)
From the first equation, y = 64 - x.
So you can substitute that for y in the second equation:
.12x + .55(64 - x) = .20(64)
This equation is linear in x, so you should have no problem simplifying and solving for x, and then using the first equation to get y.