Guided Practice

The total cost after sales tax is also proportional to the sales tax. For example, with a 6% sales tax on $80 of groceries, you would pay a total of:

($80 × 0.06) + $80

We can rewrite this using the Distributive Property in reverse as:$80 × (1 + 0.06)

So, the total cost, y, is proportional to the sales tax, like this:y = $80 × (1.06)

And the constant of proportionality is 1.06.In the video, the sales tax amount is represented by the variable .

In the sales tax equation, the constant of proportionality is %, or 0.06.

If the groceries cost $80, then the sales tax amount is $.

In the tip equation, the constant of proportionality is %, or 0.18.

If the meal costs $55, then the tip amount will be a total of $.

The cost of your meal is $62.90, and you leave a 20% tip.

Complete the equation to determine the tip amount, y, by substituting values for the variables. Write decimals to the hundredths place.

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You pay 6% sales tax on groceries which cost $104.50.

Complete the equation to determine the tax amount, y, by substituting values for the variables. Write decimals to the hundredths place.

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Your groceries cost $65.75, and your state sales tax is 8%.

Complete the equation to determine the tax amount, y, by substituting values for the variables. Write decimals to the hundredths place.

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You left a 15% tip, so the tip amount, y, was $11.25.

Complete the equation to determine the cost of the meal before tip, x, by substituting values for the variables. Write decimals to the hundredths place.

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You leave a tip of y = $5.04, which is 18% of the cost of the meal.

Complete the equation to determine the cost of the meal before tip, x, by substituting values for the variables. Write decimals to the hundredths place.

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You pay 7.8% sales tax on groceries. So, your sales tax amount is y = $11.70.

Complete the equation to determine the cost of the groceries before tax, x, by substituting values for the variables. Write decimals to the hundredths or thousandths place.

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Study the example. A total after tip is also proportional to the tip. Suppose your meal costs $55, and you leave an 18% tip. You would pay a total of:

($55 × ) + $

Use the Distributive Property in reverse to rewrite this as:$ × (1 + )

The constant of proportionality is .You pay a 15% tip in addition to a meal cost of $47.00.

Complete the equation to determine the total cost of the meal, y.

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You pay 4% sales tax in addition to $185.00 in groceries.

Complete the equation to determine the total cost of the groceries, y.

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You pay 9% sales tax in addition to $35 in groceries.

Complete the equation to determine the total cost of the groceries, y.

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You pay a 20% tip in addition to a meal cost of $14.50.

Complete the equation to determine the total cost of the meal, y.

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You pay a 15% tip in addition to a meal cost of $28.99.

Complete the equation to determine the total cost of the meal, y, to the nearest cent.

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Sometimes an item in a store can be marked with a sign like the one below.
This sign means that you can pay 25% less than the marked price. If the price of a shirt is regularly $18, and it is marked as 25% off, then the amount you save is proportional to the regular price:

$18 × 0.25 = $4.50

And the sale price is proportional to the regular price also:$18 – ($18 × 0.25)

You may also see signs that advertise that a product has 20% more of something. For example, a cereal brand may advertise that it contains 20% more fiber.

Suppose that, before the increase, a box of that cereal contained 10 grams of fiber. How much does it contain now?

10 + 10 × 0.20 = 10(1 + 0.2) = 10(1.2)

The cereal box now has 10 × 1.2, or 12, grams of fiber.

Calculate the sale price of the shirt.

$18 – ($18 × 0.25) = $

You can rewrite the sale price equation using the Distributive Property in reverse:$18 × (1 – 0.25) = $18 × 0.75

This equation says that the sale price is 75% of the regular price of $18.$18 × 0.75 = $

The coordinate plane shows the sale price graph and the amount saved graph.

The constant of proportionality for the amount saved graph is .

The constant of proportionality for the sale price graph is .

A coat that is normally $130 is on sale for 60% off. Use the graph and the equations to calculate the amount saved (y1) and the sale price (y2).

You save: = ()()

Sale price: = ()()

A pair of shoes that normally costs $60 is on sale for 30% off. Use the graph and the equations to calculate the amount saved (y1) and the sale price (y2).

You save: = ()()

Sale price: = ()()

A TV that normally costs $400 is on sale for 20% off. Use the graph and the equations to calculate the amount saved (y1) and the sale price (y2).

You save: = ()()

Sale price: = ()()

A cereal that normally has 8 grams of fiber now contains 30% more fiber. How much fiber, y, does it have now?

= ()()

A yogurt that normally has 0.4 serving of fruit now says that it has 25% more fruit. How much fruit, y, does the yogurt have now?

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Geometric figures can be proportional in size also. These triangles are proportional.

You can still find the constant of proportionality.

1.06 × ? = 1.59 or 1.1 × ? = 1.65

The constant of proportionality is 1.5. The larger triangle is 1.5 times the size of the smaller one. We can say that the larger triangle is 150% the size of the smaller one.

Determine the constant of proportionality when starting with the larger triangle and shrinking proportionally.

1.59 × ? = 1.06 or 1.65 × ? = 1.1

Round to the nearest whole percent. The smaller triangle is % the size of the larger triangle.

Calculate each constant of proportionality as a percent. Round to the nearest whole percent.

The larger rectangle is % the size of the smaller rectangle.

The smaller rectangle is % the size of the larger rectangle.

Calculate each constant of proportionality as a percent. Round to the nearest whole percent.

The larger circle is % the size of the smaller circle.

The smaller circle is % the size of the larger circle.

Calculate each constant of proportionality as a percent. Round to the nearest whole percent.

The larger square is % the size of the smaller square.

The smaller square is % the size of the larger square.

Calculate each constant of proportionality as a percent. Round to the nearest whole percent.

The larger trapezoid is % the size of the smaller trapezoid.

The smaller trapezoid is % the size of the larger trapezoid.

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

Groceries: $

Sales tax: %

Cost: $

Discount: %

Meal: $

Tip: %

Original: $

Markup: %

A proportion equation is one of the form y = kx, where k is a constant value. If you can write an equation in that form, you can say that y is proportional to x and x is proportional to y.

For example, you get 4 quarters for every dollar. We can write that as

q = 4d or d = 1/4q

The first equation means "the number of quarters is 4 times the number of dollars," and the second equation means "the number of dollars is one-fourth the number of quarters." While q and d can change (they are variables), 4 or one-fourth is constant. So, the number of quarters is proportional to the number of dollars, and the number of dollars is proportional to the number of quarters.

Use the proportion equation to complete the sentence.

a = 2b

is proportional to .

Use the proportion equation to complete the sentence.

3h = n

is proportional to .

Use the proportion equation to complete the sentence.

3/4t = v

is proportional to .

Use the proportion equation to complete the sentence.

f = 9/5c

is proportional to .

Use the proportion equation to complete the sentence.

2x = 3y

is proportional to .