Tom and Francisca each opened a savings account on the same day. Tom started by putting $839 in his account, and he will deposit an additional $475 each week. Francisca made an initial deposit of $779, and she will add $478 more each week. Eventually, Tom and Francisca will each have the same amount saved. How many weeks will that take? What is that amount?
For Tom, the total amount in his account after a certain number of weeks is given by the equation: T(w) = 839 + 475w, where w is the number of weeks.
For Francisca, the total amount in her account after a certain number of weeks is given by the equation: F(w) = 779 + 478w.
To find out when Tom and Francisca will have the same amount saved, we need to solve the equation T(w) = F(w).
839 + 475w = 779 + 478w
839 - 779 = 478w - 475w
60 = 3w
w = 20
So, it will take 20 weeks for Tom and Francisca to have the same amount saved.
To find out the amount they will have saved after 20 weeks, substitute w=20 in any of the equations.
T(20) = 839 + 475(20) = 839 + 9500 = $10339.
So, after 20 weeks, Tom and Francisca will each have $10339 saved. Answer: \boxed{20, 10339}.
Scouting troops in Johnson County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 38 crab meals and 32 vegetarian meals, with total receipts of $1,984. Another sold tickets for 38 crab meals and 34 vegetarian meals, bringing in a total of $2,032. How much do the two types of tickets cost?
Let's assume the price of a crab meal is $x and the price of a vegetarian meal is $y.
From the first scenario, we can write the equation:
38x + 32y = $1,984.
From the second scenario, we can write the equation:
38x + 34y = $2,032.
To find the prices, we need to solve this system of equations.
We can solve this system in multiple ways, but let's use the substitution method.
Let's solve the first equation for x:
38x = $1,984 - 32y.
x = ($1,984 - 32y)/38.
Now substitute this value of x in the second equation:
38(($1,984 - 32y)/38) + 34y = $2,032.
$1,984 - 32y + 34y = $2,032.
2y = $2,032 - $1,984.
2y = $48.
y = $48/2.
y = $24.
Now substitute this value of y into the first equation to find x:
38x + 32($24) = $1,984.
38x + $768 = $1,984.
38x = $1,984 - $768.
38x = $1,216.
x = $1,216/38.
x = $32.
So, the price of a crab meal is $32, and the price of a vegetarian meal is $24. Answer: \boxed{32, 24}.
Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can Margie spend on each dog for food and medication?
Let's assume the cost of supplies for a cat is $x.
Then the cost of supplies for a dog would be 2*x, as each dog's supplies cost twice as much as a cat's supplies.
Margie needs to buy supplies for 164 cats and 24 dogs, so the total cost of supplies is:
164x + 24(2x) = 4240.
Simplifying this equation, we get:
164x + 48x = 4240.
212x = 4240.
Dividing both sides by 212, we find:
x = 4240/212 = 20.
So the cost of supplies for a cat is $20.
And the cost of supplies for a dog would be 2 * 20 = $40.
Therefore, Margie can spend $40 on each dog for food and medication. Answer: \boxed{40}.
Brian hosts a podcast about computers, and Nate hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Brian released 32 episodes and Nate released 16 episodes, for a total of 4,720 minutes of content. This year, Brian released 40 episodes and Nate released 16 episodes, which lasted a total of 5,392 minutes. How long is each episode?
Let's assume the duration of each episode for Brian's podcast is x minutes.
Then the total duration of Brian's episodes last year would be 32x minutes.
The total duration of Brian's episodes this year would be 40x minutes.
Similarly, let's assume the duration of each episode for Nate's podcast is y minutes.
Then the total duration of Nate's episodes last year would be 16y minutes.
The total duration of Nate's episodes this year would be 16y minutes.
According to the problem, the total duration of all episodes last year was 4,720 minutes:
32x + 16y = 4,720.
And the total duration of all episodes this year was 5,392 minutes:
40x + 16y = 5,392.
We now have a system of two equations with two unknowns. We can solve it by substitution or elimination method. Let's use the elimination method.
Multiply the first equation by 2 to make the coefficients of y in both equations the same:
64x + 32y = 9,440.
40x + 16y = 5,392.
Subtract the second equation from the first equation to eliminate y:
(64x + 32y) - (40x + 16y) = 9,440 - 5,392.
24x + 16y = 4,048.
Now we have the equation:
24x + 16y = 4,048.
Rearrange it to solve for y:
16y = 4,048 - 24x.
16y = 16(253 - 3x).
y = 253 - 3x.
Now substitute this value of y in the first equation:
32x + 16(253 - 3x) = 4,720.
32x + 4,048 - 48x = 4,720.
Combine like terms:
-16x = 672.
Divide both sides by -16:
x = -672/16.
x = -42.
Since we are dealing with time, the duration cannot be negative. There must be an error in the data provided or in calculations. Please cross-check and verify the information given to find the correct duration of each episode.