Answer:
4 blue marbles
Skills needed: Number Theory, Fractions
Step-by-step explanation:
1) The problem tells us that the jar contains marbles that are either red, green, or blue (No Other Color).
It also mentions that [tex]\frac{2}{5} (\frac{4}{10})[/tex] of the marbles are red
and that [tex]\frac{1}{10}[/tex] of the marbles are blue
- The given statement is that 20 marbles are green, and we need to find out the number of blue marbles.
2) We need to first find out the total number of marbles, and then multiply that by [tex]\frac{1}{10}[/tex] to get the # of blue marbles.
---> Given [tex]\frac{4}{10}[/tex] are red and [tex]\frac{1}{10}[/tex] are blue, [tex]1-\frac{1}{10}-\frac{4}{10}[/tex] of the marbles are green (since fractions add up to 1 whole)
[tex]1 - \frac{1}{10} - \frac{4}{10} = \frac{9}{10} - \frac{4}{10}=\frac{5}{10}[/tex]
[tex]\frac{5}{10} \text{ is also } \frac{1}{2}[/tex]
Half the marbles are green.
3) Let's make the total marbles the variable: [tex]m[/tex]
[tex]\frac{1}{2} * m=20[/tex] ---> Since half of (of signifies multiplication) the total marbles are green.
Multiply both sides by 2 to isolate: [tex]m = 20*2[/tex], [tex]m=40[/tex]
Total number of marbles is 40.
4) After that, we multiply this by [tex]\frac{1}{10}[/tex] since one-tenth of the total is blue.
---> [tex]\frac{1}{10}*m = \frac{1}{10}*40=4[/tex]
4 blue marbles is the answer.
