Answer:
The hospital gets [tex]2.75\:\rm{mg}[/tex] of medicines from these three companies.
Step-by-step explanation:
Company A has [tex]1.3[/tex] milligrams, which is [tex]0.9[/tex] milligram more than Company C's.
If [tex]A,B,C[/tex], are the medicines produced by Companies A,B,C, respectively,
then, [tex]A=1.3\:\rm{mg}[/tex], and its expression is given as,
[tex]\begin{aligned}A&=0.9+C\\1.3&=0.9+C\\C&=1.3-0.9\\C&=0.4\:\rm{mg}\end{aligned}[/tex]
Company A has [tex]1.3[/tex] milligrams, which is twice the difference between the weight of Company B's supply and Company C's.
So, its expression is given as,
[tex]A=2(B-C)\\[/tex]
Substituting values of [tex]A,C[/tex], the expression becomes,
[tex]\begin{aligned}1.3&=2(B-0.4)\\0.65&=B-0.4\\B&=0.65+0.4\\B&=1.05\:\rm{mg}\end{aligned}[/tex]
So, the hospital gets,
[tex]\begin{aligned}A+B+C&=1.3+0.4+1.05\\&=2.75\:\rm{mg}\end{aligned}[/tex]
of medicines.
We are required to find the total milligrams if medicine the hospital can get from the three companies.
The total quantity of medicine the hospital can get from the three companies is 2.75 milligrams
There are there companies:
Company A
Company B
Company C
Company A = 1.3 milligrams
Company A is 0.9 milligrams more than Company C's
A = 0.9 + C
1.3 = 0.9 + C
1.3 - 0.9 = C
0.4 = C
C = 0.4 milligrams
Company A is also twice the difference between the weight of
Company B's supply and Company C's
A = 2(B - C)
1.3 = 2(B - 0.4)
1.3 = 2B - 0.8
1.3 + 0.8 = 2B
2.1 = 2B
Divide both sides by 2
B = 2.1/2
B = 1.05 milligrams
Therefore,
A + B + C
= 1.3 + 1.05 + 0.4
= 2.75 milligrams
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