
math (mixture problems) homework help?
can you tell me how to solve this (I have like 7 of each of these problems)?
Veronica has been saving dimes and quarters. She has 94 coins in all. The total is $19.30. How many dimes and how many quarters does she have?
The Sears Tower in Chicago is the tallest building in North America. The total height of the tower (t) and the antenna that stands on top of it is (a) 1729 feet. The difference in heights between the building and the antenna is 1171 feet. How tall is the Sears Tower?
Two stores are having a sale on T-shirts that normally sell for $20. Store S is advertising an (s) percent discount, and Store T is advertising a (t) dollar discount. Rose spends $63 for three T-shirts from Store S and one from Store T. Mannny spends $140 on five T-shirts from Store S and four from Store T. Find the discount at each store.
Thank you!
QUESTION #1
The first step in solving any problem like this is to write out the appropriate equation. In this example, because we’re talking about dimes and quarters, we will use the variables:
d= # of dimes
q= # of quarters
Because dimes are worth $0.10, we can multiply the number of dimes we have (d) by 0.10 to get the total cash value of our dimes. We will do the same for quarters (q), except they’re worth $0.25 so we multiply by that instead.
0.10*d + 0.25*q = 19.30 <--- I added together our money from dimes and quarters and set it equal to 19.30 because that is the amount of money the question said we had.
d+q=94 <--- this one is an easier equation, adding the number of dimes and quarters must give us 94 because the question says there are 94 coins in all
Now we can do some math. Okay, if we rearrange our second formula, we can solve for q and then substitute it into our first equation.
q = 94 - d <--- I subtracted d from both sides, now let's substitute this into our original equation
0.10*d + 0.25*(94-d) = 19.30 <--- distribute the 0.25 to the parenthesis
.10d + 23.5 - .25d = 19.30 <--- combine like terms (both of the d's)
-0.15d + 23.5 = 19.30 <--- subtract 23.5 from both sides to isolate -0.15d
-0.15d = -4.2 <--- divide both sides by -0.15
d = 28
Now that we know we had 28 dimes, we can plug this into either of our original equations to solve for quarters. I will use the second equation because it's easier:
q = 94 - d <--- plug in 28 for d
q = 94 - 28
q = 66
ANSWERS:
28 dimes and 66 quarters
-----------------------------------------------
QUESTION #2
t + a = 1729
t - a = 1171
Okay, we can rearrange either formula, but I will use the second one:
t = 1171 + a (I added a to both sides)
Now we plug this into the other formula:
t + a = 1729 <--- substitute 1171 + a for t
1171 + a + a = 1729 <--- combine the a's
1171 +2a = 1729 <--- subtract 1171 from both sides to isolate 2a
2a = 558 <--- divide by 2 to solve for a
a = 279
Now we can plug 279 for a in either equation:
t = 1171 + a <--- sub 279 for a
t= 1171 + 279
t = 1450
ANSWER:
The antenna is 279 feet and the tower is 1450 feet
-----------------------------------------------
QUESTION #3
I am going to set this up for you, but I will let you try the third problem on your own. All you have to do is substitute one equation into the other like I did for the first two.
Rose's equation:
63 = 3(20 - 20*s) + 1(20 - 20*t) <--- let's distribute to both of our parenthesis
63 = 60 - 60s + 20 - 20t <--- combine the numbers without the variables (remember, you can't combine -60s with -20t because the variables are not the same)
63 = 80 - 60s - 20t
Manny's equation:
140 = 5(20 - 20*s) + 4(20 - 20*t) <--- let's distribute to both of our parenthesis
140 = 100 - 100s + 80 - 80t <--- combine the numbers without the variables (remember, you can't combine -100s with -80t because the variables are not the same)
140 = 180 - 100s - 80t
Now I did most of the work for you, you just need to finish setting up your equations and then set one of them up to substitute into the second one! Good luck!
Oh and don't forget you need two numbers for your answer s and t. Once you find the first one, just plug that number into one of your equations to solve for the value of your second variable.
Flying Around the CN Tower in Toronto in a Cessna 172
|
|
Wilson Electronics Sleek Cell Phone Signal Cradle Booster for All Cell Phones with Mini Magnet Mount Antenna – For Single User $129.99 Wilson Electronics 815226 Sleek Cell Phone Signal Cradle Booster is designed to work with all cell phones. The Sleek features a signal booster a cradle and a built-in port for battery charging. The Sleek amplifies signals both to and from the cell tower and improves your cell phone?s voice and data signal strength significantly…. |
|
|
Wilson Electronics Desktop Adjustable Gain Cell Phone Signal Booster for Home or Office – For Multiple Users $359.95 WILSON 801247 3-WATT DESKTOP CELLULAR AMPLIFIER… |
|
|
Terk FM Only Stereo Antenna FM+ $7.14 The FM+ FM only Stereo Antenna Improves FM radio reception and is a great replacement antenna for ”T” wire stereo antenna…. |



