Question

On a certain hot​ summer's day, 166 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $265.00. How many children and how many adults swam at the public pool that​ day? Please help I’ve been working on this for hours

Answer 1

Answer:

134 children and 32 adults.

Step-by-step explanation:

This solution is based on guess and check, I don't know if you know this method but it's used all the time for questions like these.

Or the faster way called assumption, but it is much harder and might get careless easily.

So let's do guess and check.

Predict how much adults and children would be there.

Let's say 76 children and 90 adults.

76 x 1.50 = 114

90 x 2.00 = 180

Total for first attempt = 180 + 114 = 294

The total amount is too much, so let's lower the number of adults and increase the number of children.

Let's say 85 children and 81 adults.

85 x 1.50 = 127.5

81 x 2.00 = 162

162 + 127.5 = 289.5

Again it's too much.

Let's make it 120 children and 46 adults.

120 x 1.50 = 180

46 x 2.00 = 92

180 + 92 = 272

It's too much but almost there, let's make another one.

140 children and 32 adults.

140 x 1.50 = 210

32 x 2.00 = 64

Too much children, lower it down to 132 children and 34 adults.

132 x 1.50 = 198

34 x 2.00 = 68

198 + 68 = 266

As you can see we're quite close.

134 children and 32 adults.

134 x 1.50 = 201

32 x 2.00 = 64

201 + 64 = 265

So we finally got the answer.