Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 14 small cakes per hour. The kitchen is available for 3 hours and 29 large cakes and 260 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?

If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time.
29 large cakes are needed for the party so \(\frac{\mathrm{29} }{\mathrm{15}}\) = 1 and \(\frac{\mathrm{14} }{\mathrm{15}}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 14 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 14 x 3 = 42 small cakes during that time.
260 small cakes are needed for the party so \(\frac{\mathrm{260} }{\mathrm{42}}\) = 6 and \(\frac{\mathrm{4} }{\mathrm{21}}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 7 = 9 cooks.