# Solutions

Excellent job on today’s word problem! Are you ready to check your answer? Look below to see if your solution matches ours.

**Lower Elementary**

*Answer:*16 portraits

*Solution:*If Polly sketched twice as many as Kate, then she sketched 4 + 4 = 8 portraits. Oscar sketched twice as many as that, so he sketched 8 + 8 = 16 portraits.

**Upper Elementary***Answer:* 1¾ container*Solution:* We can find out how many containers Carlo used by dividing the amount of clay he used by the amount of clay per container. That’s 36 ÷ 16 = 2R4. Next, we can find out what fractional part of a container got used by dividing the remainder by 16 again. That’s 4 ÷ 16 = ¼. So, Carlo used 2¼ containers of clay. Now we can find that Carlo has 4 – 2¼ = 1¾ containers left.

**Middle School***Answer:* 32 photos*Solution:* Tyler already has 3 × 16 + 4 × 14 = 104 good pictures. To average 17 good pictures per roll, he needs 17 × 8 = 136 pictures to turn out in total. So, Tyler needs 136 – 104 = 32 photos on the __8th__ roll to turn out.

**Algebra and Up***Answer:* 2 fluid ounces of 30% / 70%, 2 fluid ounces of 50% / 50%, and 4 fluid ounces of white*Solution:* Right away, we know that we need 4 ounces of white paint because 50% of 8 ounces is 4 ounces. So, next we need to find out what amounts of the two purple paints to mix together to make 4 ounces of a 40% red, 60% blue paint (we need to double the percentages because we’re only dealing with the half that isn’t white). We can see that the average of 30% red and 50% red is 40% red, so we need equal parts of the first and second paints. That’s 2 ounces of each to make 8 ounces total. Alternatively, we could use the equation 50% (4 – x) + 30%x = 4(40%) wherein x represents the amount of the first paint.