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Zinaida [17]
2 years ago
14

For a charity initiative, 420 t-shirts were made; in the morning 1/3 of the t-shirts is sold and in the afternoon 4/7 of the rem

aining ones. How many shirts are left to sell at the end of the day?
Mathematics
1 answer:
KIM [24]2 years ago
7 0

1/3 * 420 = amount of t-shirts sold in the morning

1/3 * 420 = 420/3 = 140 t-shirts

140 t-shirts were sold, so remaining is 420 - 140

420 - 140 = 280 remaining t-shirts

4/7 * 280 = amount of t-shirts sold in the afternoon

4/7 * 280 = (280/7) * 4 = 40 * 4 = 160 t-shirts

160 t-shirts were sold, so remaining is 280 - 160

the remaining t-shirts = 120 t-shirts

120 t-shirts are left to sell at the end of the day

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The answer to this question is 120winners
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Does anyone understand how to do this
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Answer:

Step-by-step explanation:

I understand it!  (But I'm a high school math teacher so it might be unfair!) ; )

Anyway you have 2 numbers.  You don't know what they are so we will call them x and y.  Our first statement says that these numbers multiply to equal 120.  So that first equation is

xy = 120

Our second statement says that they add to -22.  So that second equation is

x + y = -22

Now we need to find the 2 numbers.  We have 2 unknowns, x and y.  That means that we have to have 2 equations.  No more than 2 no less than 2.  Solve the first equation for y.  It doesn't matter which equation you pick and which variable you choose to solve for.  If you do the work correctly, you will get the correct answers either way.  Solving the first equation for y gives you:

y=\frac{120}{x}

Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:

x+\frac{120}{x}=-22

Instead of finding a common denominator, we are going to eliminate x in the denominator altogether.  Do this by multiplying everything by x to get

x^2+120=-22x

Get everything on one side of the equals sign and factor:

x^2+22x+120=0

Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:

x^2+12x+10x+120=0

Use factoring by grouping now.  

(x^2+12x)+(10x+120)=0

From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:

x(x + 12) + 10(x + 12) = 0

Now factor out the common x + 12 to get a factored quadratic:

(x + 12)(x + 10) = 0

By the Zero Product Property, either x + 12 = 0 or x + 10 = 0.  Solving both for x gives you x = -12 or x = -10.

If x = -12, then

-12 + y = -22 so

y = -10

If x = -10, then

-10 + y = -22 so

y = -12.

The combinations of x and y are:

If x = -12, y = 10

If x = -10, y = -12

It doesn't matter which one is which.  They are not asking you to specifically define x and y.  They are asking you to find the numbers, and you did!

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