Karan needs to choose between two gym plans. he can either pay a \$150$150dollar sign, 150 joining fee and a \$10$10dollar sign, 10 monthly fee, or he can pay a \$50$50dollar sign, 50 joining fee and a \$30$30dollar sign, 30 monthly fee. on what month will the cumulative costs of the plans be equal, and what will those total costs be?

For the first plan:
Joining fee = $150
monthly fee = $10
Cumulative cost in x months = $(150 + 10x)

For second plan:
Joining fee = $50
monthly fee = $30
Cumulative cost in x months = $(50 + 30x)

Let the cumulative costs of both plan are equal after x months.



On 5th month, the cumulative costs will be equal.

Cost = 50 + 5×30 = 50 + 150 = $200

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Noah: 3 cupsLin: 4 cups

Step-by-step explanation:

When the 12-cup bag of sugar is divided evenly, each baker gets 6 cups.

There is no dot on Noah"s graph for 6 cups of sugar, so you have to extrapolate the given set of dots to see where it might be. You notice that each dot is 1/2 cup of flour more than the one to its left, so you expect that Noah will use 3 cups of flour for 6 cups of sugar.

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Similarly, the table for Lin does not have an entry for 6 cups of sugar. Again, the next entry can be figured using the relations between previous entries. Here, each row for sugar goes up by 1 1/2 cups, so the next row would be 4 1/2 + 1 1/2 = 6 cups. And the rows for flour go up by 1 cup, so the next row for flour (for 6 cups of sugar) would be 4 cups of flour.

Lin will use 4 cups of flour for 6 cups of sugar.

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Alternate solution

The relationship are proportional in both cases, so you can read the value for a smaller amount (2 cups or 3 cups of sugar), then multiply the value by an appropriate multiplier (3 or 2) to get the number of cups of flour for 6 cups of sugar.

Noah: 1 flour for 2 sugar ⇒ 3 flour for 6 sugar

Lin: 2 flour for 3 sugar ⇒ 4 flour for 6 sugar