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.
amount of cider added=amount of cider in mix
.12A+.55B=.22*64
A+B=64
To solve these problems, we will use the method of setting up equations and solving for the unknowns. Let's go through each problem and break down the steps to find the solution.
2. Tub A contains 12% apple cider, and Tub B contains 55% apple cider. We need to find the number of ounces of cider from each tub to make a 64 ounce drink that is 20% apple cider.
Let's assume x ounces from Tub A and y ounces from Tub B. We can set up the equation:
(0.12x + 0.55y) / 64 = 0.20
Simplifying the equation:
0.12x + 0.55y = 0.20 * 64
0.12x + 0.55y = 12.8
This gives us the first equation. For the second equation, we know that the total amount of cider should be 64 ounces:
x + y = 64
Now, we have two equations:
0.12x + 0.55y = 12.8
x + y = 64
We can solve this system of equations using substitution or elimination method to find the values of x and y.
3. Mary is running to school at a speed of 12 mph, and her little lamb leaves home 15 minutes (0.25 hours) later and runs at a speed of 17 mph. We need to find the time of day when the lamb catches Mary.
Let t be the time in hours it takes for the lamb to catch Mary. Mary has a 15-minute head start, so she has been running for t + 0.25 hours.
Distance traveled by Mary = 12 * (t + 0.25)
Distance traveled by lamb = 17 * t
The lamb catches Mary when the distance traveled by both is the same. Thus, we set up the equation:
12 * (t + 0.25) = 17 * t
Solving this equation will give us the time in hours, which we can convert to minutes and add to 7:15 AM to find the time of day when the lamb catches Mary.
4. Granny needs 3 gallons of 15% vinegar for her pickles, and Bud bought 2 gallons of 50% vinegar. We need to find the amount of pure spring water to mix with the vinegar to get a 3-gallon canner filled with a 15% solution of vinegar.
Let x be the amount of pure spring water needed.
The amount of vinegar in 2 gallons of 50% vinegar is 2 * 0.50 = 1 gallon.
The final mixture will contain 3 gallons, so the amount of vinegar in the final mixture is 3 * 0.15 = 0.45 gallons.
Since we are mixing 1 gallon of vinegar with x gallons of water, we set up the equation:
1 / (1 + x) = 0.45
Solving this equation will give us the amount of pure spring water required.
5. To find the depth of the well, we need to use the formulae "distance = 16t^2" for a falling object and "distance = 1100 * t" for the speed of sound in air.
Let t be the time it takes for the rock to fall and the sound to travel back up the well.
The rock takes t seconds to fall, so the distance traveled by the rock is given by "distance = 16t^2".
The sound takes the remaining time (7 - t) seconds to travel back up the well, so the distance traveled by sound is given by "distance = 1100 * (7 - t)".
The total distance is equal to the sum of the distances traveled by the rock and the sound. Setting up the equation:
16t^2 + 1100 * (7 - t) = total distance
Now, we can solve this quadratic equation using the quadratic formula to find the depth of the well.
7. Grandma Wilson weighs 188 pounds and needs 25 milligrams of Tylenol per 50 kilograms of body weight for an I.V. We need to find the amount of saline solution administered in ml.
First, we need to convert Grandma Wilson's weight from pounds to kilograms: 188 pounds * (1 kilogram / 2.2 pounds) = 85.45 kilograms.
The amount of Tylenol needed for Grandma Wilson's weight is (25 milligrams / 50 kilograms) * 85.45 kilograms = 42.725 milligrams.
Given that the saline medicine bottle contains 5 milligrams of Tylenol for each 9 ml of saline, we can set up the equation:
(42.725 milligrams / 5 milligrams) * 9 ml = amount of saline solution needed
Solving this equation will give us the required amount of saline solution to be administered in ml.
8. Let's assume the number of nickels is x.
Since the number of quarters is one more than the number of nickels, the number of quarters is (x + 1).
Since the number of dimes is five more than the number of nickels, the number of dimes is (x + 5).
The value in dollars of the nickels is 0.05x, the value in dollars of the dimes is 0.10(x + 5), and the value in dollars of the quarters is 0.25(x + 1).
We know that the total value is $7.95, so we set up the equation:
0.05x + 0.10(x + 5) + 0.25(x + 1) = 7.95
Solving this equation will give us the number of each type of coin.
9. We have 18 quarts of fluid in the radiator, which is currently 15% antifreeze. We need to find the amount of fluid to drain and then replace with 100% pure antifreeze to make a 40% antifreeze solution.
Let x be the amount of fluid to be drained in quarts.
The amount of antifreeze drained is 0.15x.
We want to add 100% pure antifreeze to the radiator, which is equivalent to x quarts.
The total volume of the fluid in the radiator after replacement is (18 - x) quarts.
Since the antifreeze concentration is given by (amount of antifreeze / total volume), we set up the equation:
(0.15x + 100 * x) / (18 - x) = 0.40
Solving this equation will give us the amount of fluid to drain into a disposable container and the amount of pure antifreeze to add to the radiator.