Upper and lower bounds

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Make a 2x2 table putting upper and lower bound at the top and the two objects at the side:

-------------------------

Lb | UP |

Cup | |

--------------|-----------

Bottle | |

________|_____ |__

Create 2 number lines, one for the cup, one for the bottle

The cups numberline will start at 150 ml as stated in the question

As it is to the nearest 5 ml it must be a numberline with 150 half way in a 5 number gap. So therefore it is 2.5 units either way

147.5__________150_________152.5

The second numberline is for the bottle which starts at 750 as stated in the question. Because it is to 2 significant figures, the second unit in the number is a 10, meaning there is a 10 number gap on the line.

745____________750____________755

Lower bound for the cup is 147.5

The cups upper bound will be 152.5

The bottles lower bound will be 745

The bottles upper bound will be 755

Next look at the worst situation being:

Cup is too big with least amount of lemonade

this means we must look at the numbers:

745ml (lemonade)

and

152.5 (Cups)

Divide the numbers:

745/152.5 = 4.89 (Rounded to 3 S.F.)

This is how many cups he can fill!

4.89 is less that 5!

745/152.5 = 4.885

88.5 ml is left over!

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