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If she buys one pack of bread rolls she would need 40 ham slices, so she would need to buy 2 packs of ham slices (60 slices), but 20 ham slices would be wasted. If she buys 1 pack of ham slices she would need 15 bread rolls, so she would need to buy 1 pack of bread rolls, but 5 bread rolls would be wasted.

If she buys 3 packs of bread rolls (60 rolls) she would need 120 ham slices, which is exactly 4 packs of ham slices. And if she buys 4 packs of ham slices (120 slices) she would need 60 bread rolls, which is exactly 3 packs of bread rolls. So whichever way you look at it, she would need to pay 3×£2.87+4×£6.32=£8.61+£25.28=£33.89. The ratio of packs of rolls:packs of slices is 3:4.

To make exactly 90 sandwiches she would need to buy 90 rolls and 180 slices. 90 rolls=4½ packs; 180 slices=6 packs. If nothing was to be wasted, she could buy 9 packs of rolls (180 rolls) and 12 packs of slices (360 slices) at a cost of 9×£2.37+12×£6.32=£97.17. Then she could make 180 sandwiches.

If wastage is allowed, and she had to make more than 90 sandwiches, she would need more than 6 packs of ham slices. 7 packs would give her 210 slices, needing 105 rolls, so she would need more than 5 packs of rolls. With 5 packs of rolls she would have enough to make 100 sandwiches, but she would need 200 slices, more than 6 packs. 5 packs of rolls and 7 packs of slices would give her enough to make 100 sandwiches, but she would waste some ham. The cost would be 5×£2.37+7×£6.32=£56.09, wasting 10 slices of ham.

 

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