To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3

Christine scored 75% on the test meaning she earned 75% of the possible points on the test. There were 180 possible points on the test so she earned 180 x 0.75 = 135 points. Each question is worth 3 points so she got \( \frac{135}{3} \) = 45 questions right.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-4x² + 3x²
(-4 + 3)x²
-x²

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 have in common.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{6} \) = 5\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 17 x 2 = 34 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{34} \) = 13\(\frac{14}{17}\) 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 6 + 14 = 20 cooks.