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Question

On a certain hot summers day, 287 people used the public swimming pool. The daily prices are 1.50 for children and 2.50 for adults. The receipts for admission totaled 621.50 how many children and how many adults swam at the public pool that day

Answer 1

This is a system of linear equations with two constraints:

1. Since there are 287 people who went swimming, one constraint is the sum of children (c) plus adults (a), which is c + a = 287
2. The cost per child times number of children that went swimming plus the cost per adult times the number of adults that went swimming must total 621.50, so we also have: 1.5*c + 2.5*a = 621.50.

Now we have two equations and two unknowns:

(i) c + a = 287

(ii) 1.5*c + 2.5*a = 621.50

Let's eliminate c by multiplying the equation (i) by -1.5. We get:

-1.5*c - 1.5*a = -430.5

Now we can add it to equation (ii) to get:

a = 191

Substitute the answer for a into equation (i):

c + 191 = 287

We get c = 96.

Answer 2

Hi Abigail L.

96 children

191 adults

You can use a system of equations to solve your problem by substitution or elimination.

Let x = children

Let y = adults

Equation 1 for total attendance

x + y = 287

y = 287 - x

Equation 2 for total receipts

1.50x + 2.50y = 621.50

We can put this in terms of a single variable x, by substituting for from equation 1 above

1.50x + 2.50(287 - x ) = 621.50

1.50x + 717.50 - 2.50x = 621.50

1.50x - 2.50x + 717.50 = 621.50

-x + 717.5 = 621.50

-x = -717.50 + 621.50

-x = -96

x = 96

y = 287 - 96 = 191

Checking

1.50(96) + 2.5(191) = 621.50

144 + 477.50 = 621.50

I hope this helps.

Answer 3

We can solve this using a system of equations.

Let a = number of adults

Let c = number of children

a + c = 287 - the number of adults and children together is 287

Each adult pays $2.50. 1 pays $2.50. 2 pays $2.50 + $2.50. 3 pays $2.50 + $2.50 + $2.50. So we have repeated addition, or multiplication.

2.5a is the amount paid by the adults.

In a similar way, 1.5c is the amount paid by the children

2.5a + 1.5c = 621.5 - the total money paid.

Here is our system

a + c = 287

2.5a + 1.5c = 621.5

Let's solve using substitution. If we solve the top equation for a by subtracting c from both sides we get

a = -c + 287

Let's substitute this expression for a into the bottom equation.

2.5(-c + 287) + 1.5c = 621.5 - distribute the 2.5

-2.5c + 717.5 + 1.5c = 621.5 - combine like terms

-c + 717.5 = 621.5 - subtract 717.5 from both sides

-c = -96

c = 96

Plug this value into a = -c + 287

a = -96 + 287

a = 191

There were 191 adults and 96 children at the pool.

Check

191 adults + 96 children = 287 total

191($2.50) + 96($1.50) = $621.50