Respuesta :
Answer:
6.75g
Step-by-step explanation:
The first step is converting everything to grams, by rules of three. Then we add.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: 0.0025kg to g
Each kg has 1000g, so:
1kg - 1000g
0.0025kg - xg
x = 1000*0.0025 = 2.5g
0.0025kg = 2.5g
Second step: 1750 mg
Each g has 1000mg, so:
1g - 1000mg
xg - 1750mg
1000x = 1750
[tex]x = \frac{1750}{1000}[/tex]
x = 1.75g
1750 mg = 1.75g
2.25g - OK
Third step: 825,000 μg to g
Each g has 1,000,000 ug, so:
1g - 1,000,000 ug
xg - 825,000 ug
1,000,000x = 825,000
[tex]x = \frac{825,000}{1,000,000}[/tex]
x = 0.25g
825,000 μg = 0.25g
Final step: adding everyting
0.25g + 2.25g + 1.75g + 2.50g = 6.75g
Taking into account the change of units, the sum results in 7.325 g.
Rule of three
The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
The direct rule of three is the rule applied in this case where there is a change of units.
To perform in this case the conversion of units, you must first know that 1 kg= 1000 g, 1 mg= 0.001 g and 1 μg=1×10⁻⁶ g. So:
- If 1 kg is 1000 g, 0.0025 kg equals how many g?
1 kg ⇒ 1000 g
0.0025 kg ⇒ x
So: [tex]x=\frac{0.0025 kgx1000 g}{1 kg}[/tex]
Solving:
x= 2.5 g
So, 0.0025 kg is equal to 2.5 g.
- If 1 mg is 0.001 g, 1750 mg equals how many g?
1 mg ⇒ 0.001 g
1750 mg ⇒ x
So: [tex]x=\frac{1750 mgx0.001 g}{1 mg}[/tex]
Solving:
x= 1.75 g
So, 1750 mg is equal to 1.75 g.
- If 1 μg is 1×10⁻⁶ g, 825000 μg equals how many g?
1 μg ⇒ 1×10⁻⁶ g
825000 μg ⇒ x
So: [tex]x=\frac{825000 ugx1x10^{-6} g}{1 ug}[/tex]
Solving:
x= 0.825 g
So, 825000 μg is equal to 0.825 g.
Now you add all the values in the same unit of measure:
2.5 g + 1.75 g + 2.25 g + 0.825 g= 7.325 g
Finally, the sum results in 7.325 g.
Learn more with this example:
https://brainly.com/question/24534599
