Math Question?

Question

1. The sum of two numbers is 36 and their difference is 16. Please work this out and show me the steps to acheiving the right answer-please! This isn't the orginal question so please show steps so I can do it right.

2. Bob runs a fruite stand, selling boxes of fruite. He sells Oranges for $11/a box, and grapefruite $10/box. He sold 762 boxes toltal, and his income was $8125. How many boxes of Oranges did he sell?
I want to add the $11 and $10 and then divide by $8125, but I don't think it's right. HELP!

Can someone please help me out with these:) Math's not my strong suite!

Thanks everyone who gave me great work. I actually did them right (yeahhhh). I was thinking I did them wrong but, nope they are correct! Thanks everyone:)

Answer 1

let x and y be the two numbers
x+y = 36
x-y = 16

add the two eq
2x = 52 x = 26; y = 10

Let x be the cost of a box of orange
y = cost of a box of grapefruit

x+y = 762
11x + 10y = 8125

x (1) by 11
11x + 11y = 8382
y = 257
x = 505

check 11*505 + 10*257 = 8125

Answer 2

First you think about the possible pairs of numbers. Since the total of the added numbers is 36 and the difference between the numbers is 16, if one number is 35, then the other number (16 lower) is 19. But 19 and 35 is 54, which is way too high.

So, experiment lower. Try 25 and 6 (25 - 16). You will see that 25 and 6 is 31, which is too low. So choose a new number, one that is a little higher than 25. Then add that number and the one which is 16 lower. When you find two which add up to 36, you have found it!

Regarding your second question, you have just found out the use of algebra! Woo hoo!

11x + 10y = $8125
x + y = 762

Do you see how I got that? You know that __ of the $11 boxes and ___ of the $10 boxes, add up to $8125. So I named one 11 times x (written shortcut as 11x) and the other 10y. You know that the number of orange boxes plus the number of grapefruit boxes equals 762, because the problem gave you that clue.

Remember the trick to playing with equations? You can play around with the equation as long as you perform the same act to BOTH sides of the equation.

11x + 10y = $8125

What makes this hard is that there are two mystery numbers, x and y. But you don't have to get stuck this way! Because you know that x + y = 762, you can change the y number into an x number.

You remember that whatever you do to one side of the equation, you have to do to the other side, right?

So if you subtract x from both sides you get y = 762 - x

So slip 762 - x into the y place in your equation and it will look like this. 11x + 10 (762 - x) = 8125

This equals 11x + 7620 (from 10 times 762) -10x (from 10 times - x) = 8125

So your new equation is 11x + 7620 - 10x = 8125

Rearranged it to be 11x-10x + 7620 = 8125

Simplify it to be 11x - 10x + 7620 = 8125

Simplify it further to 11x - 10x = x + 7620 = 8125

Subtract 7620 from both sides of the equation and you get
x = 8125 - 7620 = 505 or x= 505

Let's check this to make sure we didn't make a mistake.

505 times $11= $5555

If 505 of the boxes were oranges then 257 were grapefruit (because 505 + 257 = 762 boxes) And 257 times $10 is $2570

$2570 + 5555 = $8125.

You know all of the answers now - how many boxes of oranges, how many boxes of grapefruit, and how much he made from the sale of each. But the problem only asks about oranges.

So look back and you'll see that the oranges were the $11/box fruit (no "e" on fruit) and he sold 505 boxes of oranges.

I broke this way down to show each part. The important thing to learn is NOT the answer. It's how to make the problem into an equation - that was the part where I wrote the word problem as 11x + 10y = 8125. The next part was to figure out how to state the problem is either x or y, and eliminate the other from the equation.

Once you do that, it's just back to basic math. Let me know if it helped.

Answer 3

OK - let's try this:

x + y = 36
x - y = 16 ; add the two equations (notice the y's go away)

2x = 52
x = 26

NOw substitute in the first : 26 + y = 36 ;
y = 10

Now check in the second
26 - 10 = 16??
16 = 16
===============
OK same principle here

o + g = 762
11o + 10 g = 8125 ; multiply top by 10

10o + 10 g = 7620
11o + 10 g = 8125 ; subtract bottom and g goes away

- o = -505
o = 505

Substitute
505 + g = 762 ; g = 257

Now final check
11(505) + 10(257) = 8125??
5555 + 2570 = 8125??
8125 = 8125 YES!!

Hope that helps!

Answer 4

These are called linear combination or substitution problems. You have to let x and y represent numbers. For the first one, (we will use linear combinations which is cancelling one of the variables out) you can make the two equations x+y=36 and x-y=16... Add the two together, and the y's cancel, leaving 2x=52 which means x=26. Plug 26 into either of the original equations to get y=10..... On the second problem, I used substitution... This is done by solving for one of the variables... First, lets make 2 equations 11x+10y=8125 and x+y=762 (the variables stand for the number of boxes sold)..... I solved the second equation for x, x=762-y... I can then plug this into the other equation ----> 11(762-y) + 10y = 8125.... 8382--11y+10y=8125 .... -y=-257 so y=257... Plug that back into either original equation to get x=505... 505 orange boxes sold and 257 grapefruit boxes sold. Hope this helps :)

Answer 5

PROBLEM 1:
X + Y = 36 (THE SUM OF TWO NUMBERS IS 36)
X - Y = 16 (THEIR DIFFERENCE IS 16)
ADD THE TWO EQUATIONS VERTICALLY.
THE +Y CANCELS THE -Y, SO:
2X = 52
X = 52/2
X = 26
NOW SUBSTITUTE THE VALUE OF X IN ANY OF THE ORIGINAL EQUATIONS. THE FIRST ONE, FOR EXAMPLE:
X + Y = 36
BUT X = 26, SO:
26 + Y = 36
Y = 36 - 26
Y = 10
FINAL ANSWER: X=26 AND Y=10
THE TWO NUMBERS AND 26 AND 10

PROBLEM 2:
(R=ORANGES G=GRAPEFRUITS)
R + G = 762 (ALL THE BOXES BOB SOLD = 762)
11R + 10G = 8125
(ORANGE BOXES @ $11 + GRAPEFRUIT BOXES @ $10 = 8125)
SO YOUR EQUATIONS ARE:
R + G = 762
11R + 10G = 8125
IF YOU TIME THE WHOLE FIRST EQUATION BY -10, YOU WILL BE ABLE TO ELIMINATE THE G, SO:
-10R - 10G = -7620
11R + 10 G = 8125 (JUST WRITING THE 2ND EQUATION UNDER
ADDING BOTH EQUATIONS VERTICALLY,
11R - 10R + 10G - 10G = 8125 - 7620
THE G CANCELS AND YOU GET:
R = 505
NOW SUBSTITUTE THIS VALUE OF R IN THE FIRST EQUATION:
R + G = 762
505 + G = 762
G = 762 - 505
G = 257
FINAL ANSWER:
505 ORANGE BOXES AND 257 GRAPEFRUIT BOXES
BEST WISHES!

Answer 6

1. the answer is 26 and 10.
x+y=36 and x-y=16. Add the equations. You get 2x = 52. Therefore x=26 and y is 10.
2. 11x + 10y = $8125 and x + y = 762. Multiply the 2nd equation by 11 to get 11x + 11 y = 8382. Subtract the first equation from the 2nd one and get y=257. Therefore x=505. He sold 505 boxes of oranges.

Answer 7

Large number=(sum+difference)/2=(36+16)/2=26
therefore the smaller number is 10

11x762=8382
8382-8125=257
257/1=257
there fore 257 grapefruit box, 505 orange boxes

Answer 8

"sum of two numbers is 36": x + y = 36
"their difference is 16": x - y = 16
Add the two equations to eliminate the y terms:
2x = 52
x = 26
x + y = 36 so y = 10
---------------
O = boxes of oranges sold
G = boxes of grapefruit sold

income = 11*O + 10*G = $8125

O + G = 762 Multiply eqn by -10 and add to previous eq to eliminate G terms

11*O + 10*G = 8125
-10*O - 10*G = -7620
------------------------------
O = 505
Bob sold 505 boxes of oranges

Answer 9

1.
x + y = 36
x - y= 16

x = 16 +y

then substitute this in...
16+y + y = 36
2y = 10 y= 5
then substute 5 into y
x + 5 = 36
x= 31


2. x = # of grape fruit
y = # of oranges

x + y = 762

11y + 10x = 8125

see if u can work this one out, substitute what x = (y- or + whatever)

then solve to find y, then change y to the number

Answer 10

I can help with the first question. First, you set it up into two equations based on the given information:

x + y = 36
x - y = 16

Solve for one variable in one equation:
x = 16 + y

Substitute this into the other equation, and solve for the variable:
(16 + y) + y = 36
16 + 2y = 36
2y = 20
y = 10

Now that you have one variable, plug it into one of the original equations to solve for the other variable.
x + 10 = 36
x = 26

So, x = 26 and y = 10.