1. 1x + 1y = 12 ⇒ 14x + 14y = 168
14x + 10y = 140 ⇒ 14x + 10y = 140
4y = 28
4 4
y = 7
14x + 10(7) = 140
14x + 70 = 140
-70 -70
14x = 70
14 14
x = 5
(x, y) = (5, 7)
A. five adults and 7 children
2. x + y = 4
x - y = -6
2x = -2
2 2
x = -1
-1 + y = 4
+1 +1
y = 5
(x, y) = (-1,5)
C. (-1,5)
3. x + y = 178 ⇒ 0.1x + 0.1y = 17.8
0.1x + 0.25y = 29.8 ⇒ 0.1x + 0.25y = 29.8
-0.15y = -12
-0.15 -0.15
y = 80
0.1x + 0.25(80) = 29.8
0.1x + 20 = 29.8
-20 -20
0.1x = 9.8
0.1 0.1
x = 98
(x, y) = (98, 80)
D. 98 dimes and 80 quarters
