We will let cc denote the price of a package of crocus bulbs, and tt denote the price of a package of tulip bulbs. From Danielle's sale, we are given:
4t+4c = $764t+4c=$76 (E1)
And from Heather...
1t+11c=1691t+11c=169 (E2)
To solve this system of equations, we can either perform the operation E1-4E2E1−4E2, or E2-(1/4)E1E2−(14)E1. This latter will prove to be easier. Thus...
1/4 E1 -> 1/4(4t+4c) = 1/4(76) -> t+c=1914E1→14(4t+4c)=14(76)→t+c=19
E2-1/4E1 -> (1t+11c)-(t+c)=(169-19) -> 10c = 150 -> c = $15E2−14E1→(1t+11c)−(t+c)=(169−19)→10c=150→c=$15
Then plugging back into our 1/4 E114E1 equation...
t+c=19 -> t+15=19 -> t = $4t+c=19→t+15=19→t=$4
Double check these in both equations...
E1 -> 4(4)+4(15) = 16+60 = $76E1→4(4)+4(15)=16+60=$76
E2 -> 1(4)+11(15) = 4 + 165 = $169E2→1(4)+11(15)=4+165=$169
