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Alecsey [184]
3 years ago
14

Leonardo makes the following purchases at the store: 1 backpack for $16.89 5 spiral notebooks for $1.19 each 1 pack of mechanica

l pencils for $3.68 2 packs of lead refills for $1.88 each Leonardo has 2 coupons, each for 45 cents off on the purchase of a pack of lead refills. The coupons are applied after tax and the sales tax is 5% of the purchase. If Leonardo paid $30.89 , then he _____ for his purchase. a. did not pay enough b. paid the correct amount c. paid $0.04 too much d. paid $0.57 too much
Mathematics
2 answers:
Alex787 [66]3 years ago
6 0
I believe the correct answer is he paid the right amount

vovikov84 [41]3 years ago
3 0

Answer:

Option B is correct choice.

Step-by-step explanation:

1 backpack for $16.89

5 spiral notebooks for $1.19 each so total cost = 5*1.19=5.95

1 pack of mechanical pencils for $3.68

2 packs of lead refills for $1.88 each so total becomes =2*1.88=3.76

Total becomes : 16.89+5.95+3.68+3.76=$30.28

Sales tax on the purchase = 5 % the value is 0.05*30.28=1.514

Now total cost becomes = 30.28+1.514 = $31.794

Leonardo has 2 coupons, each for 45 cents off on the purchase of a pack of lead refills. That means he got 90 cents off on both packs. So, new total Leo has to pay is : 31.794-0.90 = $30.894

Hence, Leo paid $30.89 in total. So, he paid the correct amount.

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\huge{\mathbb{ \tt{ANSWER}}}

I shall use the symbol U for union

^ for intersection

~ for complement

<h3 /><h3>----------------------------------------------------------------------------------------------------</h3>

The property of set subtraction states that for any sets X and Y, X-Y = X ^ Y~

That is in words, X throw away Y is the same as the intersection of X and the complement of Y

or X and anything NOT in Y

At the SET level, the proof looks like this:

(P-Q) U (Q-P) = « given

(P^Q~) U (Q ^ P~) = « property of set subtraction

(P U Q) ^ (P U P~) ^ (Q~ U Q) ^ (Q~ U P~) = « distributive property

(P u Q) ^ (Q~ U P~) = « Union of any set with it's complement is the universal

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(P u Q ) ^ (Q ^ P)~ = « De Morgan's Law

(P u Q) - (Q ^ P) = « property of set subtraction

(P u Q) - (P ^ Q) « commutative property

<h3>----------------------------------------------------------------------------------------------------</h3>

At the ELEMENT level, the proof looks like this:

» Proves left side is subset of right side

If x is in (P-Q) U (Q-P) then x is in (P-Q) OR x is in (Q-P)

If x is in P-Q then x is in P but not in Q.

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Since x is not in Q, x is NOT in P ^ Q

Hence x is in P U Q but NOT in P^Q, which

means it is an element if (P U Q) - (P ^ Q)

Therefore x is an element of the set defined by the right side, which means (P-Q) U (Q-P) is a subset of (P U Q) - (P ^ Q)

« proves right side is subset of the left side

If x is an element of (P U Q) - (P ^ Q) then

x is in (P U Q) but NOT in (P^Q)

Since x is in P U Q, x is in P OR x is in Q.

Since x is NOT in (P^Q) then x is NOT in BOTH P and Q.

Hence x is in either P or Q but not both.

If x is in P, then x is not in Q, so x is in P-Q.

Therefore x is in (P-Q) U (Q-P).if x is in Q, then x is not in P, so x is in Q-P.Therefore x is in (Q-P) U (P-Q).There x is an element of set defined by the left side, which menas (P u Q)-(P ^Q) is a subset of (P-Q) U (Q-P).

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