580 people used the swimming pool. The prices are $ 1.75 for kids and $ 2.50 for adults. The receipts for admission totaled $1192. How many kids and adults swam at the pool that​ day?

Answer 1

Hey!

Let's just go over the information we have. 580 total people. $1192 total. $1.75 per kid, $2.50 per adult. I think it would be helpful to write equations for all the things we know.

Total number of people is 580:

1. we know kids and adults came to this pool so we can write the following equation: k + a =580
2. k = kids and a = adults

The receipts for the admissions totaled: $1192

1. we know the prices of the tickets: $1.75 for kids, $2.50 for adults
2. we also know that both kids and adults came, we just don't know how many total of them came. So we can write this equation: 1.75k + 2.5a = 1192

Now that we have our equations...

k + a =580

1.75k + 2.5a = 1192

we have to solve for each variable. It is a bit easier to work with our first equation. Let's rewrite it to get a variable alone. Let's start by figuring out how many adults came to the pool.

580 - a = k (we subtracted "a" because we know that from 580 people, some were kids and we don't know how many of them there are.)

Now, the trick to these problems is to use the equation we rewrote and plug it in to the other equation!

Our other equation is: 1.75k + 2.5a = 1192

Let's plug in our rewritten equation for "k" (since it is an equation that equals k):

1.75(580-a) + 2.5a = 1192

simplifies to:

1015-1.75a +2.5a = 1192

let's isolate "a"

1015 - 1015 - 1.75a + 2.5a = 1192 - 1015 (we subtracted 1015 from both sides since what you do to one side you must do to the other)

simplify:

-1.75a+2.5a = 177

0.75a = 177

divide both sides by 0.75 (so we can isolate "a")

a = 236

Now, let's plug it in to the original equation: 580 = k + 236

Let's isolate "k": 580 -236 = k +236 - 236 (subtracting 236 from both sides)

Result: k = 344

Lastly, to check our answers: Lets plug in our answers to the second equation (since we know already that 236+ 344 = 580 . If we are right, our answer for total amount of money should be $1192)

1.75k + 2.5a = 1192

k = 344

a = 236

we sub in the variables:

1.75(344) + 2.5 (236) = 1192

602 + 590 = 1192

1192 = 1192

We were right!!!

I hope this helps!

Take care and best of wishes!

(If you need any more help, feel free to reach out!)

Answer 2

K+ A =580

1.75K + 2.50A = 1192

1.75K + 1.75A = 1.75(580)

(2.5-1.75)A = 1192 - 1.75(580)=1192-580-3(145=1192-580-435=1192-1015=177

A=177/.75= (4/3)177=4(59=236

A= 236= Adults

K = 580-236= 344 Kids

check the answer

1.75(344)+2.5(236) = 1192

Answer 3

Let a = number of adults

Let k = number of kids

a+k = 580

a = 580-k

1.75k +2.50a = 1192

1.75k +2.5(580-k)=1192

1.75k-2.5k + 1450 = 1192

-0.75k = -258

k = -258/-0.75 = 344

a = 480-344 = 236