To order certain plants from a catalog, it costs $3.00 per plant......

One of the questions that can be solved using back-solving

Pick answer choice C to be the number of plants.

20*3 = 60

60 * 5/100 = 3

60 + 3 + 6.95 = 69.95

69.95 = 3x+0.05*3x+6.95
x = 20
Ans. C

Let 'n' number of plants were ordered.

Total cost of plants: n * 3 = 3n

Sales tax: 5% of 3n = \(\frac{5}{100}\) * 3n = \(\frac{3n}{ 20}\)

Shipping: 6.95

Overall bill: 69.95

=> 3n + \(\frac{3n }{ 20}\) + 6.95 = 69.95

=> 3n + \(\frac{3n}{20}\) = 63

=> \(\frac{63n }{20}\) = 63

=> n = 20

Answer C

Solution:

Let p = the number of plants the company ordered. Thus, the cost of the plants only will be 3p. We multiply by 1.05 to include the sales tax in our calculation. The value 6.95 is a flat fee that is not taxed. Thus, we can create the equation:

3p * 1.05 + 6.95 = 69.96

3p * 1.05 = 63

3p = 60

p = 20

Answer: C

To order certain plants from a catalog, it costs $3.00 per plant, plus a 5 percent sales tax, plus $6.95 for shipping and handling regardless of the number of plants ordered. If Company C ordered these plants from the catalog at the total cost of $69.95, how many plants did Company C order?

My approach:

Subtract the shipping: $69.95 - $6.95 = $63

Plant after tax = $3.15

10 plants after tax = $31.50
20 plants after tax = $63

Answer is C.

Note = 1.05 is equivalent to 21/20

Putting things in fraction is easier for direct multiplication problems.

As soon as you want to start setting up an equation with a variable even though there's no variable in the question, that's a sign to use PITA (Plugging in the Answers).

11% of the PS questions in the 2022 OG Quant book can be solved using PITA, making it the second-most useful test-taking technique.

Out of answer choices B, C, and D, which looks easiest to work with (with rare exception, start with B, C, or D since they typically give more information than A and E)?

I'll go with C.

Okay, so there are 20 plants at $3 each. That's $60. We need to add tax. 10% would be $6, and we want 5%, so $3. Now we need to add shipping. That's $6.95. So, $60 for the plants + $3 for tax + $6.95 for shipping. That's $69.95. Is that what we wanted? Sure is. Done.

Answer choice C.

ThatDudeKnowsPITA

but how are we sure sales tax is calculated as tax per unit or if it is calculated on the overall amount, is 63 in our case

The $63 is the amount already including tax. 20 plants at $3 per plant is $60 before tax. We need to add 5% tax to that, and 5% of $60 is $3, so that's where the $63 comes from.

You could have calculated tax per item and then added them up. That works, too. For each $3 plant, you'd have needed to add $0.15 for tax ($0.15 is 5% of $3). That makes each plant $3.15 including tax, so 20 of them cost $63.

Let's denote the number of plants Company C ordered as "x".

The total cost for the plants can be calculated as follows:
Cost of plants = Number of plants * Cost per plant = x * $3.00

Sales tax is 5% of the cost of plants:
Sales tax = 0.05 * Cost of plants = 0.05 * (x * $3.00)

Shipping and handling cost is a flat fee of $6.95.

So, the total cost for Company C can be calculated as:
Total cost = Cost of plants + Sales tax + Shipping cost
Total cost = x * $3.00 + 0.05 * (x * $3.00) + $6.95

Given that the total cost is $69.95, we can set up the equation:
$x * 3.00 + 0.05 * (x * 3.00) + 6.95 = 69.95$

Simplify the equation:
$3.00x + 0.15x + 6.95 = 69.95$

Combine the x terms and solve for x:
$3.15x + 6.95 = 69.95$
$3.15x = 63.00$
$x = 63.00 / 3.15$
$x = 20$

So, Company C ordered 20 plants.

I thought you had to apply tax rate at the end??? People here are multiplying the 5% tax to individual 3 dollars…and then multiplying by the number of flowers bought…. That’s allowed???

total cost = $69.95 ~ $70.00 (Rounding off)
70*5%=$3.5 => 70-3.5 =67.5 (5 percent sales tax)
67.5-6.95=60.65 (5 for shipping and handling)
60.65/$3= 20.21 (per plant cost)

OA=20