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Help please im stuggling

Help please im stuggling-example-1

1 Answer

3 votes

Answer:

715 mL

Explanation:

You want the total volume in two containers that have the volume ratio 4:7 and a difference in volumes of 195 mL.

Ratio units

Considering the question in terms of "ratio units," we see the difference of ratio units is 7-4 = 3, and the total of ratio units is 7+4 = 11. Then the total volume will be 11/3 times the difference in volume:

total volume = (11/3)(195 mL)

total volume = 715 mL

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Additional comment

Though it is not necessary, as a check you can work out the volumes of the containers. The smaller will be 4/3 times the difference: 260 mL, and the larger will be 7/3 times the difference: 455 mL. The total is ...

455 +260 = 715 . . . mL

and the difference is ...

455 -260 = 195 . . . mL

If you prefer to work with equations for the volume, you can let x and y represent the volumes of the smaller and larger containers. Now you have ...

x/y = 4/7

y -x = 195

Substituting for y gives ...

x/(195 +x) = 4/7

7x = 4(195) +4x

3x = 4(195) ⇒ x = (4/3)·195 . . . . as above

Then the total volume is ...

x+y = 195 +2x = 195(1 +2·4/3) = 11/3·195 . . . as above

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