Faith observed 16 bugs while doing research for her science project. She observed insects and spiders, which had a total of 114 legs. Bearing in mind that insects have 6 legs and spiders have 8 legs, how many insects did she observe?

A. 7
B. 8
C. 9
D. 10

Question

Faith observed 16 bugs while doing research for her science project. She observed insects and spiders, which had a total of 114 legs. Bearing in mind that insects have 6 legs and spiders have 8 legs, how many insects did she observe?

A. 7
B. 8
C. 9
D. 10

hero · Answer

x = spiders
y = insects

x + y = 16
8x + 6y = 114

hero · Answer

Can you solve from there or no?

anonymous · Answer

What numbers could I use to substitue for x and y?

anonymous · Answer

7, 8, 9, 10?

hero · Answer

y = 16 - x
y = (114-8x)/6

y = y

6(16 - x) = 114 - 8x
96 - 6x = 114 - 8x
8x - 6x = 114 - 96
2x = 18
x = 9
y = 7

istim · Answer

I think you should try them all?

hero · Answer

so 7 insects total

hero · Answer

Well, amongst them, you know that they should add to get 16 so if you had to guess, it would be between 7 and 9 as far as guessing answer choices

hero · Answer

But using algebra, we don't have to guess

anonymous · Answer

Lol okay. Thank you Hero :-)