On a certain hot summer's day, 225 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $435.25. How many children and how many adults swam at the public pool that day?

Step-by-step explanation:

Let us represent:

Number of children = x = 59

Number of Adults = y = 166

On a certain hot summer's day, 225 people used the public swimming pool.

x + y = 225

x = 225 - y

The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $435.25.

$1.75 × x + $2.00 × y = $435.25

1.75x + 2y = 435.25

We substitute 225 - y for x

Hence:

1.75(225 - y ) + 2y = 435.25

393.75 - 1.75y + 2y = 435.25

Collect like terms

-1.75y + 2y = 435.25 - 393.75

0.25y = 41.5

y = 41.5/0.25

y = 166 Adults

Note that:

x = 225 - y

x = 225 - 166

x = 59 children

Hence, the number of children is 59 and the number of Adults is 166

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°