Respuesta :
Answer:
5:6 + 7:8 = 12:14
Jan will have 12 marbles
Kim will have 14 marbles
Jan and Kim own 40 and 48 marbles respectively.
Important information:
- Jan and Kim has marbles in ratio 5:6.
- Jan gains 2 more marbles and the ratio is 7:8.
We need to find the initial number of marbles each own.
Ratio:
Let the initial number of marbles be [tex]5x[/tex] and [tex]6x[/tex].
Jan gains 2 more marbles and the ratio is 7:8. So,
[tex]\dfrac{5x+2}{6x}=\dfrac{7}{8}[/tex]
[tex]8(5x+2)=7(6x)[/tex]
[tex]40x+16=42x[/tex]
Isolate the variable.
[tex]16=42x-40x[/tex]
[tex]16=2x[/tex]
[tex]\dfrac{16}{2}=x[/tex]
[tex]8=x[/tex]
Now, find the initial number of marbles.
[tex]5(8)=40[/tex]
[tex]6(8)=48[/tex]
Therefore, Jan and Kim own 40 and 48 marbles respectively.
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