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A designers spring line focuses on silk dresses, some with zippers an 13 Oct 2023, 23:13
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Dresses with zippers: 450 Dresses with buttons: 400
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55% (03:46) correct 45% (03:53) wrong based on 226 sessions

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Data Insights (DI) Butler 2023-24 [Question #39, Date: Oct-13-2023] [Click here for Details]

A designer’s spring line focuses on silk dresses, some with zippers and some with buttons. The dresses require an average of five yards of silk each, for which the designer paid $28 per yard. In addition, zippers cost $2 each, and the necessary decorative buttons were $ 1.50 each. If each dress requires six buttons or one zipper, and the total expense for fabric and notions was $123,500, how many dresses of each type can the designer produce?
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Dresses with zippers: 450 Dresses with buttons: 400
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GMAT Focus 1: 735 Q90 V89 DI81
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A designers spring line focuses on silk dresses, some with zippers an 07 Apr 2024, 09:49
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AyushiMarwaha
Is there a shorter way of solving this apart from plugging in values?
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­The equation is 142x+149y = 123500

If x and y were equal, x= y = 123500/(142+149) = 123500/291 = 424

Thus, choose two numbers that will give sum close to 424*2 or 848

350 and 500 is one option and 400 and 450 is the other.

Further 142x+149y = 123500 tells us that 149 has to be multiplied by a number ending with 00, otherwise you will not get 123500

Two cases you have to check now

142*350+149*500 = 71*2*350+149*500 = 71*700+149*500...The left most non zero digit will be 7*1+9*5 or 52 or 2.
Thus our answer is 142*450+149*500 = 71*2*450+149*400 = 71*900+149*400...The left most non zero digit will be 9*1+9*4 or 45 or 5.
The above is incase we do not use calculator.

Otherwise, knowing solution is 142*350+149*500 or 142*450+149*400, one can solve the question with working out on any one equation

The solution may seem longish, but that was for understanding. Use of number properties can help you home down to 2-3 options. ­
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A designers spring line focuses on silk dresses, some with zippers an 17 Oct 2023, 02:17
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Can Someone explain this?

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A designers spring line focuses on silk dresses, some with zippers an 17 Oct 2023, 03:42
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Cost of dress with Zipper- 142* 450= 63900
Cost of dress with button- 149*400= 59600

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A designers spring line focuses on silk dresses, some with zippers an 23 Oct 2023, 18:18
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kahixa
Let's set up some equations to solve this problem. Let X represent the number of dresses with zippers and Y represent the number of dresses with buttons.

The total expense for fabric and notions can be calculated using the following equation:

Total Expense = Cost of Fabric + Cost of Zippers + Cost of Buttons

The cost of fabric is given as $28 per yard, and each dress requires 5 yards of silk, so the cost of fabric for X dresses with zippers and Y dresses with buttons is:

Cost of Fabric = 28 * 5 * (X + Y)

The cost of zippers is $2 each, and each dress with zippers requires one zipper. So, the cost of zippers for X dresses with zippers is:

Cost of Zippers = 2 * X

The cost of buttons is $1.50 each, and each dress with buttons requires 6 buttons. So, the cost of buttons for Y dresses with buttons is:

Cost of Buttons = 1.50 * 6 * Y

Given that the total expense for fabric and notions was $123,500, we can write the equation:

123,500 = 28 * 5 * (X + Y) + 2 * X + 1.50 * 6 * Y

Now, we can simplify this equation:

123,500 = 140 * (X + Y) + 2X + 9Y

123,500 = 140X + 140Y + 2X + 9Y

123,500 = 142X + 149Y

Now, we need to find the number of dresses with zippers (X) and the number of dresses with buttons (Y) that satisfy this equation.

To make this problem easier to solve, we can rearrange the equation to isolate one of the variables. Let's isolate X:

142X = 123,500 - 149Y

X = (123,500 - 149Y) / 142

Now, we need to find integer values for X and Y that make the equation true and non-negative. We'll start by trying different values for Y and see if we can find corresponding values for X:

Let Y = 0:
X = (123,500 - 149 * 0) / 142
X = 123,500 / 142 ≈ 869.01

Y = 0 doesn't give us an integer value for X, so let's try Y = 1:

X = (123,500 - 149 * 1) / 142
X = (123,500 - 149) / 142
X ≈ 869.46

Still not an integer. Let's try Y = 2:

X = (123,500 - 149 * 2) / 142
X = (123,500 - 298) / 142
X ≈ 868.75

Y = 3:

X = (123,500 - 149 * 3) / 142
X = (123,500 - 447) / 142
X ≈ 867.25

This process continues until we find integer values for X and Y that satisfy the equation. You can keep trying different values of Y until you find a combination that works. Keep in mind that both X and Y should be non-negative since you can't have a negative number of dresses.
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After setting up:
X = (123,500 - 149Y) / 142

You can plug in the answer choices and work from there.
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A designers spring line focuses on silk dresses, some with zippers an 07 Apr 2024, 06:29
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Is there a shorter way of solving this apart from plugging in values?
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