Painting Portraits

Algebra Level 1

Paula Picasso makes her living by painting. She paints small portraits for $20, large landscapes for $50, and masterpieces for $1000.

Paula's goal is to make at least $2800. She has already sold 1 masterpiece and 23 landscapes. How many portraits must she sell to reach her goal?

The answer is 33.

4 solutions

Desrivina Ramkas
Aug 5, 2014

We know that $1$ masterpiece $=$ $\$1000$ and $23$ landscapes $=$ $23 \times \$50$ $=$ $\$1150.$ Thus, so far, she has earned $\$1000$ $+$ $\$1150$ $=$ $\$2150.$

She needs to earn an additional $\$2800$ - $\$2150$ $=$ $\$650,$ so the number of portraits $P$ must satisfy $\$20 \cdot P \ge \$650$

which is equivalent to $P \ge 32.5.$ Since she can't sell half a painting, she must sell at least 33 portraits to meet her goal.

she can sell half of her portrait?

Geno Atup - 6 years, 10 months ago

i did the addition wrong, lol i got 2250 so i kept trying 30 and 29 and 27

dhevin N - 6 years, 9 months ago

ok i was writing 32 .5 instead of 32,5

Gunjit Kalra - 6 years, 10 months ago

no, you can't sell half a portrait so the answer is 33 not 32.5, sorry

Brett Hartley - 6 years, 9 months ago

you're right

deepthi prakash - 6 years, 10 months ago

There is nothing in the statement of the problem that says she can't paint more landscapes. Another masterpiece would overshoot, but there is room for more landscapes. I assumed that the problem meant that because 650 was not divisible evenly by 20, we had to find the combinations of landscapes and portraits that would be exactly $650. Five portraits bring in one hundred dollars, and 550 is evenly divisible by 50. I think this problem is badly stated.

David Dorenfeld - 3 years, 11 months ago

31 is correct answer. pl read the question before answer for 33.

Tatikonda Ravi Kishore - 6 years, 10 months ago

From her already sold paintings, she has gathered $2150. However, she must reach at least $2800. If she were to sell 31 small portraits, she would obtain $620 and $2150 + $620 = 2770. Clearly insufficient of the required $2800.

Eric Huan - 6 years, 10 months ago

Kabir Bagai
Aug 6, 2014

23(50)+1000+20x=2800 1150+1000+20x=2800 2150+20x=2800 20x=650 x=32.5 Round 32.5 up to get 33

If she wants to make 'at least' $2800/- only one master piece of $1k needs to be sold. Alternatively, since she had already sold 1+23 paintings and made $2150/- she has to make up only $650/-. Therefore she can sell 11 landscapes for $550/- and 5 small portraits @$20 to make $100/- So all she needs to do , is to to sell 16 (11+5) paintings to precisely meet the target. Of course,13 landscapes, if sold can fetch her $ 650/-

Jagan mohan rao - 6 years, 10 months ago

the question says how many portraits must she sell

Brett Hartley - 6 years, 9 months ago

Arpit Dadda
Aug 5, 2014

Well, there must be something wrong with the answer. I got answer 32.5 and rounded off to 33 to get correct answer. 1 master pc - 1000$ 23 landscape - 23x50$ = 1150$ Total 2150$ She need to meet total of 2800$ 2800$-2150$ = 650$/20$ = 32.5

Arpit,she can not sell 32 and a half portrait, so the answer must be 33

randa M - 6 years, 10 months ago

But then she will not be making $2800 but more than that which is contardictory to the data given

Nikhil Tandon - 6 years, 10 months ago

Getting $2810 is still reaching a goal of $2800.

Brian Nieves - 6 years, 10 months ago

Alright it says at least and it didnt say exactly

Malik Ikhraiwesh - 6 years, 10 months ago

she'll not sell a portrait for $10. the problem says "at least $2800"

Edwin Reyes - 6 years, 10 months ago

Another point is she doesn't have to sell any portraits if she sells the other products. My first answer was 0 because of the problems wording.

Jerry McKenzie - 4 years, 5 months ago

Well then Paula's goal should've been "to make at least 2800$ a week". And the question should've been "...minimum number of potraits must she sell to reach her goal?"

hanif robbani - 6 years, 10 months ago

it is profit to get 10$as pocket money for her.is it

Jeswin George - 6 years, 10 months ago

J Preethi Cheenu
Aug 10, 2014

"at least $ 2800"....there lies the solution

Painting Portraits

The answer is 33.

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