Question

1. 45% of a number is 64. what is the number?$\frac{45%}{100%}=\frac{64}{x}LXB0x=142$8. 14 of the students in grade 8 at central high school prefer basketball over hockey. if there are 49 grade 8 students at the school, what percent prefer hockey?$\frac{x}{100%}=\frac{14}{49}$$49x=1400$$\frac{49x}{49}=\frac{1400}{49}$$x=28%$

Explanation:

Step1: Set up percent proportion

Let $x$ = the unknown number.
$$\frac{45}{100} = \frac{64}{x}$$

Step2: Cross-multiply to solve

$$45x = 64 \times 100$$
$$45x = 6400$$

Step3: Isolate $x$

$$x = \frac{6400}{45}$$
$$x = \frac{1280}{9} \approx 142.22$$

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Step1: Set up percent proportion

Let $p$ = the desired percentage.
$$\frac{p}{100} = \frac{14}{49}$$

Step2: Cross-multiply to solve

$$49p = 14 \times 100$$
$$49p = 1400$$

Step3: Isolate $p$

$$p = \frac{1400}{49}$$
$$p = \frac{200}{7} \approx 28.57$$

Answer:

1. The number is $\frac{1280}{9}$ (or approximately 142.22)
2. The percentage is $\frac{200}{7}\%$ (or approximately 28.57%)