A ratio of 5:7 means out of 12 books, 5 are in one category and 7 are in another. (The “category” isn’t specified in this problem.)
So here we’re STARTING with 36 books; we want to find a ratio that is equal to 5:7 and adds up to 36. Well 36 = 3(12), and so if we multiply each number in the ratio by 3 as well, we might get what we want. Doing that gives us 15:21, which adds up to 36 and is equal to 5:7. Boom, that’s the answer.
P.S. Here’s a question you can think about: why do ratios stay the same when you multiply each number by the same amount? (For example, why is 3:1 the same as 6:2?)
Answer:
Step-by-step explanation:
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This figure has four points labeled, 2 rays which you can see labeled and one right angle. The rays are named Ray BA, and Ray BD, The right angle is angle ABD, or angle ABC. A ray has one and point and goes on forever in the other direction which is indicated with an arrow. A right angle measures 90°. You can potentially put any number of points on a line. Angles can also be named by the vertex.
3x - 17 = 9x + 7
Rearrange on same sides
-17 - 7 = 9x - 3x
-24 = 6x
Divide by 6 on either sides to isolate 6
6 and 6 cancels out
-4 = x
Answer is:
B. x = -4
Reason: if you subtract 3 on both sides of the equal sign that will leave you with 7.