James bought 32 bolts at the hardware store for a total of $12.00. some were 3−inch bolts that cost 36 cents each and the others were 4−inch bolts that cost 42 cents each. how many 3−inch bolts did james buy?

Given:
32 bolts for a total of $12.00
3-inch bolt costing 36 cents or 0.36
4-inch bolt costing 42 cents or 0.42

let x represent 3-inch bolt costing 36 cents
let y represent 4-inch bolt costing 42 cents

x + y = 32
0.36x + 0.42y = 12

x = 32 - y

0.36(32-y) + 0.42y = 12
11.52 - 0.36y + 0.42y = 12
-0.36y + 0.42y = 12 - 11.52
0.06y = 0.48
y = 0.48/0.06
y = 8

x = 32 - y
x = 32 - 8
x = 24

James bought 24 pcs of the 3-inch bolt and 8 pcs of the 4-inch bolt.

To check

0.36x + 0.42y = 12
0.36(24) + 0.42(8) = 12
8.64 + 3.36 = 12
12 = 12