Question
Marcy bought one pair of jeans at 70% off and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans and she spent a total of $84, what was the original price of the jeans?
I am having no clue on how to solve this problem? How to write the equations and solve for it?
On
The idea for "word problems" is to turn the information into mathematical statements (often, equations) about unknown quantities, and then use mathematical methods to solve for the unknown quantities.
The unknown quantities are the prices of the the jeans and the blouse. Because there are two prices for each (before and after the discounts), let's be definite and choose the variables
$$J = \textrm{original price of jeans}$$ $$B = \textrm{original price of blouse}$$
(note that, in the end, we are being asked to find the value of $J$). If we need to represent the discounted prices of these items, we don't need new variables. We know the discounted prices are
$$0.30J = \textrm{discounted price of jeans}$$ $$0.60B = \textrm{discounted price of blouse}$$
(remember, $0.70J$ is taken off the price of the jeans, so only $0.30J$ remains to be paid; similarly for the blouse).
Now represent the facts as statements.
First, the discounted cost of the blouse (in dollars) is $12$ more than the discounted cost of the jeans:
$$\underbrace{0.60B}_{\textrm{disc. blouse price}} = 12 + \underbrace{0.30J}_{\textrm{disc. jeans price}}$$
Second, the total paid is 84:
$$\underbrace{0.60B + 0.30J}_{\textrm{total paid}} =84$$
So you know
$$0.60B =12+0.30J$$ $$0.60B + 0.30J = 84$$
Now the first equation lets you represent the discounted cost of the blouse in terms of the discounted cost of the jeans; it says $12+0.30J$ is exactly the same thing as $0.60B$. So replacing $0.60B$ with $12+0.30J$ in the second equation, we can say $$(12+0.30J)+0.30J = 84$$ Now this is easily solved for $J$ (which is our goal, the original price of the jeans): $$12+0.30J + 0.30 J = 84$$ $$12+0.60J=84$$ $$0.60J = 72$$ $$J = 72/0.60$$ $$\boxed{J=120}$$
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