# Jonny and Jane are keeping murder hornets in jars under their beds. Jonny's jar has 36 hornets and weighs 4 milligrams (mg). Jane has the exact same type of jar, but she has 900 hornets that weigh 12 milligrams (mg). How much does each murder hornet weigh?

Jonny and Jane are keeping murder hornets in jars under their beds. Jonny's jar has 36 hornets and weighs 4 milligrams (mg). Jane has the exact same type of jar, but she has 900 hornets that weigh 12 milligrams (mg).
How much does each murder hornet weigh?
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Demi-Leigh Barrera
ZLet h milligrams be the weight of each murder hornet and j milligrams be the weight of the jar when its empty. The total weight of the jar is then the total weight of the hornets plus the weight of the jar when its empty.
Jonny's jar has 36 hornets so the total weight of the hornets is 36h mg. The total weight of the jar is then (36h+j) mg. Since the total weight of the jar is 4 mg, then 36h+j=4.
Jane's jar has 900 hornets so the total weight of the hornets is 900h mg. The total weight of the jar is then (900h+j) mg. Since the total weight of the jar is 12 mg, then 900h+j=12.
You then have the system of equations $\left\{36h+j=4,900h+j=12\right\}$
When solving a system of equations, use the elimination method or the substitution method. The substitution method is the best method to use when one of the equations can be easily solved for a variable. The elimination method is the best to use when you can't easily solve an equation for one of the variables. It is also the best method to use when the equations have the same or opposite coefficients for one of the variables.
The two equations have the same coefficients of 1 for the jj terms so the elimination method is the best to use to solve this system. Subtract the two equations to eliminate the jj terms. Then solve for h:
900h+j=12
$-\left(36h+j=4\right)$
__________$h=\frac{8}{864}$
$h=\frac{1}{108}$
Each murder hornet then weighs $\frac{1}{108}$ mg