Question

1. each sheet cake requires 3 cups of flour and 2 cups of sugar. if a bakery has 75 cups of flour and 75 cups of sugar, how many sheet cakes can be made? will there be any ingredients left over? explain.

1. select all the expressions that are rational numbers.

$square$ 3.14159...
$square$ $-9.1234567123...$
$square$ 9.293847210103938...
$square$ $\frac{22}{7}$
$square$ $-26$

1. the ratio of the number of model cars that jim owns to the number of model cars terrence owns is $8:6$. terrence owns 36 model cars.

how many model cars does jim own?
will the ratio change if jim and terrence each sell ten of their model cars? explain.

Explanation:

Problem 6

Step1: Calculate max cakes from flour

$\text{Max cakes (flour)} = \frac{75}{3} = 25$

Step2: Calculate max cakes from sugar

$\text{Max cakes (sugar)} = \frac{75}{2} = 37.5$

Step3: Determine limiting ingredient

The smaller value (25) is the total cakes possible.

Step4: Calculate leftover sugar

$\text{Leftover sugar} = 75 - (25 \times 2) = 75 - 50 = 25$

Rational numbers can be written as $\frac{a}{b}$ where $a,b$ are integers ($b
eq0$). Terminating/non-terminating repeating decimals, integers, and fractions of integers are rational. Non-repeating non-terminating decimals are irrational.

• $3.14159...$ is non-repeating/non-terminating (irrational)
• $-9.1234567123...$ (repeating pattern of 123, rational)
• $9.293847210103938...$ is non-repeating/non-terminating (irrational)
• $\frac{22}{7}$ is a fraction of integers (rational)
• $-26$ is an integer (rational)

Step1: Set up proportion for Jim's cars

Let $J$ = Jim's cars. $\frac{J}{36} = \frac{8}{6}$

Step2: Solve for $J$

$J = 36 \times \frac{8}{6} = 36 \times \frac{4}{3} = 48$

Step3: Check ratio after selling 10 cars

New counts: Jim has $48-10=38$, Terrence has $36-10=26$. New ratio: $\frac{38}{26} = \frac{19}{13}$. Original simplified ratio: $\frac{8}{6} = \frac{4}{3}$. $\frac{19}{13}
eq \frac{4}{3}$.

Answer:

25 sheet cakes can be made. There will be 25 cups of sugar left over (no flour is left over, since $25 \times 3 = 75$ cups of flour are used exactly).

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Problem 7