child admission is $5.80 an adult admission is $9.30. on Monday 130 tickets were sold for a total sales of $946.50. how many adult tickets were sold that day.

Question

Number of adult tickets 

Answer 1

X = child tix

Y = adult tix

 

X + Y = 130 <--- 130 were sold

 

5.80X + 9.30Y = 946.50 <--- total sales were 946.50

 

Solving the first equation for Y and multiplying the second equation by 100 to clear the decimals,

the system becomes:

 

Y = 130 - X

580X + 930Y = 94650

 

Plugging the first equation into the second:

 

580X + 930( 130 - X) = 94650

 

580X + 120900 - 930X  = 94650

 

Moving everything to the right side, changing the signs:

 

0 = 94650 - 580X - 120900 + 930X

 

0 = 350X -26250 

 

X  = 26250/350 = 75

 

75 child tix were sold ---> 55 adult tix were sold.

 

75 x 5.80 + 55 x 9.30 = 946.50 <--- YES it works!