Question 6 of 15 Next
Toward the middle of the harvesting season,
peaches for canning come in three types, early.
late, and extra late, depending on the expected
date of ripening. During a certain week, the data
to the right were recorded at a fruit delivery
station. Complete parts (a) through (d) below.
36 trucks went out carrying early peaches:
62 carried late peaches;
57 carried extra late peaches,
23 carried early and late,
30 carried late and extra late,
13 carried early and extra late,
4 carried all three:
7 carried only figs (no peaches at all).
(a) How many trucks carried only late variety peaches?
trucks
(Type a whole number.)
(b) How many carried only extra late?
trucks
(Type a whole number.)
(c) How many carried only one type of peach?
trucks
(Type a whole number.)
(d) How many trucks (in all) went out during the week?
trucks
(Type a whole number.)

answer is x<

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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