A certain brand of house paint must be purchased either in quarts at $

Question

A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

PS47402.01

A. $54
B. $60
C. $66
D. $90
E. $144

PS47402.01

ZoltanBP · Accepted Answer

Let B and W be the amounts of blue and white paints to be used, respectively.

1 qt = 0.25 gal

B:W:Total = 3:2:5

Total = 3 gal
B = 3(3/5) = 9/5 = 1.8 gal
W = 3-1.8 = 1.2 gal

The cheapest way is to buy 2 gallons of blue and 1 gallon and 1 quart of white paint.

3(18)+12 = $66

Answer: C

ScottTargetTestPrep · Answer

Since 3 gallons = 12 quarts, we can create the equation:

3x + 2x = 12

5x = 12

x = 12/5 = 2.4.

So the painter needs 4.8 quarts = 1 gallon and 0.8 quarts of white paint and 7.2 quarts = 1 gallon and 3.8 quarts of blue paint.

However, the white paint must be purchased in 1-gallon cans and 1-quart cans, so the cheapest cost of the white paint is 18 + 12 = 30 dollars. One the other hand, the blue paint is cheaper when purchased in two 1-gallon cans (instead of one 1-gallon can and four 1-quart cans), so the cheapest cost of the blue paint is 2 x 18 = 36 dollars.

Therefore, the minimum expenditure for the two colors of paint is 30 + 36 = 66 dollars.

Answer: C

sunny91 · Answer

ZoltanBP , Can you please share the approach. I wan not able to understand the solution. If 4 quarts=1 gallon,so , price for each gallon of we use quarts is 48$.

ZoltanBP · Answer

Since it's cheaper to buy a 1-gallon can of paint at $18 than four 1-quart cans of paint at 4 x 12 = $48, the rational way is to buy the integer part of the necessary amount of a certain color in 1-gallon cans. If the fractional part is not greater then 0.25 gallon then the rational choice for that part is a 1-quart can at $12. However, if the fractional part is greater than 0.25 gallon, then the rational choice is another 1-gallon can at $18 because even two 1-quart cans would cost more than $18.

Thus, he should buy two 1-gallon cans of blue paint and one 1-gallon can and one 1-quart can of white paint.

sunny91 · Answer

ZoltanBP , thanks for the reply. However, I am not able to understand the last part-
he should buy two 1-gallon cans of blue paint and one 1-gallon can and one 1-quart can of white paint.

If the total quantity to purchase 3 gallons, then he is already buying the 2 gallons of blue. So, 1 more ie. the fractional part is bought by quarts. How is there an additional one 1-gallon can.

ZoltanBP · Answer

He needs 1.8 gallons of blue paint. The integer part is 1, so following the rational strategy he will buy a 1-gallon can of blue paint to deal with it. The fractional part is 0.8, which is greater than 0.25, so he will buy an additional 1-gallon can of blue paint instead of buying four 1-quart cans of blue paint to deal with the fractional part.

He needs 1.2 gallons of white paint. The integer part is 1, so following the rational strategy he will buy a 1-gallon can of white paint to deal with it. The fractional part is 0.2, which is not greater than 0.25, so he will buy a 1-quart can of white paint instead of buying an additional 1-gallon can of white paint to deal with the fractional part.

His total purchase will be three 1-gallon cans of paint (2 blue and 1 white) and one 1-quart can of paint (white).

Thus, his total cost will be 3(18)+12 = $66.

dabaobao · Answer

Color = Blue : White : Total
Ratio = 3 : 2 : 5
Quantity = 1.8 : 1.2 : 3

To find min value for purchase:

For blue => 2 gallon => $18 * 2 = $36
For white => 1 gallon + 1 quart => $18 + $12 = $30

Least amount of money needed: $66

ANSWER: C

Akp880 · Answer

A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

PS47402.01

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

Explanation: As blue: green=3:2 which implies,
Painter needs 1.8 gallon blue and 1.2 gallon white paint (as per information given ) so ---

1) 0.8 gallon blue--- will be rounded to either 1gallon (18$) or 4 quarts(12$*4)
Lesser will be 1 gallon purchase i.e 18$

2) 0.2 gallon white--- will be rounded to either 1gallon (18$) or 1 quarts(12$)
Lesser will be 1 quarts purchase i.e 12$

Hence we will need 2 gallons Blue and (1 gallon+ 1 quarts) white paint 
Overall cost= (18*2)+(18+12)
=66

Hence C is the correct answer.

Regards,
Atul Pandey

piyushluniya · Answer

Given,
for any color:
12$/quarts(Q)
18$/gallon(G)
Also, 4Q=1G
i.e 1Q = 0.25G

total required = 3G(3 parts blue(B) and 2 parts white(W))
So, Requirement of Blue (B)= (3/5)*3 = 9/5 = 1.8G
Requirement of White (W)= (2/5)*3 = 1.2G

So, For Blue, either we can buy 1G and 4Q or 2G(question says we need to purchase sufficient quantity, so it doesn't matter if there is abit extra)

Cost of Blue 1G+4Q = 18+48 = 66
Cost of Blue 2G = 36
36 < 66

For White, either we can buy 1G and 1Q(1.25G) or 2G(question says we need to purchase sufficient quantity, so it doesn't matter if there is abit extra)

Cost of Blue 1G+1Q = 18+12 = 30
Cost of Blue 2G = 36
30 < 36

So minimum amount required = 30+36 = 66(answer)

Hope this helps.
Thanks

Afn24 · Answer

avigutman  Sir, I dont understand how to approach this. Could you please help

avigutman · Answer

There are many moving pieces here so it's a tough problem to unpack. The highlighted parts below can be very distracting, and we have to basically ignore them until we're ready for them: 
If you just focus on the non-highlighted sentence,  Afn24 , and pretend that you're the painter, what inference would you make?

SaquibHGMATWhiz · Answer

Prima facie, one may think 1 quart is costing $12 and 1 gallon (4 quarts) is costing $18 so why should we even buy a 1-quart pack?
 Of course, if we need exactly one quart, then it does not make sense to buy a gallon and waste $6. That is basically the central idea of this question

3 Gallon = 12 Quarts and we have the blue and white in the ratio 3: 2.
 Blue = \frac{3}{5}  × 12  = 7.2
 White = \frac{2}{5}  × 12  = 4.8

Now when we try to buy 7.2 quarts, we should buy 2 gallons at for $36
But when we buy 4.8 quarts we should not buy 2 gallons but we should buy 1 gallon and 1 quart and that costs us $30.

That makes the answer 36 + 30 = $66.

Option C.

siddhantvarma · Answer

Given 4 quarts = 1 gallon => 0.4 gallon = 1 quart

The key information here to understand is that you can buy gallons in whole numbers only for $18/gallon. If you have, say 5.4 gallons you’ll have to buy 6 gallons at $18/gallon which totals 6x18 = $108. However, here you can use the 0.4 gallon to buy a quart at $12/quart so now you’ll need to pay 5x18 + 1x12 = 90 + 12 = $102. Clearly using quarts and gallons together here is cheaper.

Now back to the question:

We have a 3 gallon mixture, which has 3 parts blue and 2 parts white
This means our 3 gallon mixture is a total of 5 parts => 1 part = 3/5 gallon each
So 3 parts blue is: 3x(3/5) = 9/5 gallons => 1.8 gallons => 1 gallon, 2 quarts
And 2 parts white is: 3x(2/5) = 6/5 gallons => 1.4 gallons => 1 gallon, 1 quart

So for the blue part, we can buy 1 gallon at $18/gallon and 2 quarts at $12/quart => 18 + 12*2 => $42
However, if we simply buy 2 gallons instead of this, we’ll get it at 2*($18/gallon) => $36 
This is cheaper, so we’ll buy 2 gallons only for the blue part

Now for the white part: We can buy 1 gallon at $18/gallon and 1 quart at $12/quart => $30

Hence, minimum amount needed: $66

jishnu94 · Answer

why can't we buy 1.8 gal blue and 1.2 gal white?

Bunuel · Answer

Because paint is only sold in whole quarts or whole gallons, you cannot just buy 1.8 gallons of blue and 1.2 gallons of white directly. Please review the discussion above.

caldorridge · Answer

The key is breaking the mixture into exact quantities and then matching those amounts to the cheapest purchase options.

A 3-gallon mix with a 3:2 ratio means 5 total parts. Each part equals 3 ÷ 5 = 0.6 gallon.
Blue paint needed: 3 × 0.6 = 1.8 gallons
White paint needed: 2 × 0.6 = 1.2 gallons

Since a full gallon at $18 is far cheaper than buying quarts, the smartest approach is to cover as much as possible with gallons and only use quarts when the leftover amount is small. For blue, two 1-gallon cans give 2 gallons, which safely exceeds 1.8 gallons for $36. For white, one 1-gallon can plus one quart gives 1.25 gallons, just over the 1.2 gallons needed, for $30.

That brings the minimum total cost to $66.

This kind of calculation is very practical in real painting jobs. Professional crews in Singapore often plan paint purchases this way to avoid waste and overspending, which is something discussed often by contractors offering Painting Service Singapore solutions. Clear quantity planning is also a reason why service providers referenced on:paintingservicesingapore.sg emphasize accurate measurements before buying paint.

So the second reply’s conclusion is correct, and the math behind it ensures the least amount of money is spent while still meeting the exact mixture requirement.

A certain brand of house paint must be purchased either in quarts at $

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A certain brand of house paint must be purchased either in quarts at $

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