Percent word problems
Another percent example Word problem solving strategies from chapter 3 of ck12.org Algebra I book
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- Let's do some more practice word problems.
- Patricia is building a sand box for her daughter.
- It is to be 5 feet wide and 8 feet long.
- So let me draw that.
- So the 5 feet wide-- it is to be 5 feet wide.
- So there you go.
- That's 5 feet right there.
- And 8 feet long.
- I'll do that in orange.
- 8 feet long.
- So this is like if we're looking down
- into the sand box.
- 8 feet long.
- So the sand box, if we're looking down on it, would look
- something like that.
- That would be 5 feet.
- And this side over here would also be 8 feet.
- All right, she wants the height of the sand box to be 4
- inches above the height of the sand.
- OK.
- So if we were to draw the sand box like this-- so if you were
- to draw it-- so that's 8.
- That distance right there is 5 feet.
- And then there is some height, which I think we're going to
- have to figure out.
- Let me draw the whole box just like that.
- The sand is going to fill a certain
- amount of the sand box.
- So the sand is going to fill maybe until right over there.
- So that's how much the sand is going to fill of the sand box.
- All of that is sand.
- And she wants the height of the sand box to be 4 inches
- above the height of the sand.
- So she wants this distance right here, the amount that
- the height goes above the sand, itself, to be 4 inches--
- or a third of a foot, depending how you want to
- think about it.
- Now she has 30 cubic feet of sand.
- She has 30 cubic feet of sand.
- So this sand right here is 30 feet cubed.
- How high should the sand box be?
- So this information right here, the volume of the sand,
- tells us, using it, we can figure out how high the level
- of the sand will be.
- Let's do it this way.
- Let's call l-- let me just use x.
- Let's say x is the height of the sand.
- x is equal to height of sand.
- So the total volume of our sand is going to be the height
- of the sand times the length of the box.
- Times 8 times the width of the box.
- Times 5.
- And this is going to be the total volume which they told
- us is 30 cubic feet.
- It is 30 cubic feet.
- We're taking x feet times 8 feet times 5 feet.
- So we'll get 30 feet cubed if we were to keep
- track of the units.
- So what is this?
- 8 times 5 is 40.
- So we get 40x is equal to 30.
- If we divide both sides by 40-- both sides of the
- equation by 40-- let me do that.
- You divide both sides by 40, you get x is equal to-- that
- just becomes an x.
- X is equal to 30/40, where it equals 3/4 of a foot.
- So this right here is going to be 3/4 of a foot.
- Now what is 3/4 of a foot?
- Let's see, 3/4 of a foot.
- We know that there are 12 inches per foot.
- The feet cancel out.
- 12 times 3/4 is what?
- You can divide the 12 by 4 and get a 3.
- Divide the 4 by 4 and you get a 1.
- You get 3 times 3.
- This is 9 inches.
- 9 inches.
- So the height of the sand right there is 9 inches.
- Now she wants the height of the sand box to be 4 inches
- above the height of the sand.
- So this is 9 inches.
- She wants 4 more inches.
- So what she wants the height of the sand box-- it should be
- the 9 inches of the height of the sand plus 4, which is
- equal to 13 inches.
- And we are done.
- Let's do the next problem.
- It was a sale day in Macy's, and everything was 20% less
- than the regular price.
- Peter bought a pair of shoes.
- And using a coupon, he got an additional 10%-- let me do
- that in a different color.
- He got an additional 10% off the discounted price.
- The price he paid was $36.
- The price he paid for the shoes-- let me do that in a
- different color-- the price he paid for the shoes was $36.
- How much did it originally cost?
- So let's just use-- so x is equal to original cost. There
- was just a regular sale on that day.
- Everything was 20% less than the regular price.
- So using that information, on that day, if you wanted to buy
- the shoes, the cost of the shoes would be x minus 0.20x,
- which is equal to 0.8x, right?
- If you have 20% off of a price, you're going to be
- paying 80% of the original price.
- So this is the price that everyone would have paid
- without a coupon.
- And that's what that line is telling us right there.
- Now Peter got a pair of shoes, and using a coupon, got an
- additional 10% off of this.
- An additional 10% off of that.
- So he's paying 10% less than this.
- Or another way to think of it is, he only had to pay 90% of
- this price.
- If you take 0.8x and from that you subtract 10% of this-- so
- from that, you subtract 10% of that-- of 0.8x, this is the
- same thing.
- All right.
- This is a 1 time 0.8x.
- This is the same thing as 1 minus 0.1.
- So this is the same thing.
- This is equal to 90% of 0.8x.
- And it might actually be very natural for you to
- go straight to this.
- It's natural for me.
- If I'm paying 20% less than the regular price, that means
- I'm going to pay 80% of the regular price.
- And if I get an additional 10% off of that, that means I'm
- only going to pay 90% of that.
- So this is what he's going to pay.
- And they tell us that price is $36.
- That price is equal to $36.
- So if we want to figure out x, well, we could
- multiply 0.9 times 0.8.
- Let's do that.
- So 0.9 times 0.8.
- 9 times 8 is 72.
- We have two numbers behind the decimal.
- One, two.
- So it's 0.72.
- So you get 0.72x is equal to 36.
- Or maybe we could say 72/100 x is equal to 36.
- Or we could even say this is same thing as-- what is it?
- That's the same thing as 36/50, right?
- 36/50 x is equal to 36.
- And this isn't even in lowest common forms. This is the same
- thing as 18/25.
- But I like this number because I have a 36 here.
- And so I can multiply both sides by the inverse of this.
- 50/36 times this.
- I have to do to both sides of the equation.
- 36's cancel out.
- 50's cancel out.
- 36's cancel out.
- And you're left with x is equal to $50.
- The shoes originally cost $50.
- Next question.
- Rosa has saved all year, and wishes to spend the money she
- has on new clothes and a vacation.
- She will spend 30% more on the vacation then on the clothes.
- So let's say, let's say that C is amount spent on clothes.
- She's going to spend 30% more on the vacation.
- So let's say V is equal to the amount spent on vacation.
- Well, they just told us that the vacation-- she's going to
- spend 30% more than on the clothes.
- So the vacation is going to be equal to the amount she spends
- on the clothes plus 30% of the amount she
- spends on the clothes.
- And this is the same thing as 1.3.
- 1.3 times the amount she spends on the clothes.
- That's how much she's going to spend on the vacation.
- Now, if she saved $1,000 in total, how much money, to the
- nearest whole dollar, can she spent on the vacation?
- So between V and C, she can only spend $1,000.
- So V, vacation, plus her clothes can only be $1,000.
- So we know what the vacation is in terms of the clothes.
- We can do a little substitution.
- The vacation is going to be 1.3 times the clothes.
- So we can substitute there.
- So you have 1.3 times the clothes.
- That's the vacation expenditure, plus the amount
- she spends on the clothes is equal to 1,000.
- This is 1.3 plus 1 is 2.3, times the amount she spends on
- clothes will be equal to $1,000.
- Divide both sides by 2.3.
- I'll get the calculator out for this one.
- So we have 1,000 divided by 2.3 is equal to $434.78.
- So C is equal to-- I already forgot the number-- 434.78.
- $434.78.
- So if that's the amount she spends on clothes, the rest of
- her money is going to be spent on a vacation.
- So her vacation is going to be 1,000 minus this.
- So her vacation expenditure is going to
- be 1,000 minus $434.78.
- I'll do the calculator for this one.
- Let's see.
- Let's make this into a negative number.
- And then, let's add 1,000 to it.
- And we get $565.22.
- And I'll leave it up to you to check it.
- This is how much she spends on the vacation.
- These add up to $1,000.
- And this should be exactly 30% more than this amount, the
- amount she spends on her clothes.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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