inomath

The latex for me doesn't work. I can't copy and paste the questions into the latex bar. It just makes more junk.

x = number of 9 dollar shirts. y = number of 11 dollar shirts. z = number of 12.50 dollar shirts. 

x + y + z = 23. 9x +11y +12.5z=243. 

z = 2y. 

We can replace the z with 2y. Our new equation becomes 9x +11y +12.5(2y)=243. Which becomes 9x + 11y + 25y. Which finally becomes 9x + 36y = 243. Now we can just use smart guess and check. If y = 1, x has to become 23. This doesn't work because it has to add up to 23. It will add up to 26.  x+3y has to equal 23. If y = 3, x = 9. That is too little. So we try y = 2, x = 19. This is still too much. So...there is no solution to this problem. Unless I did something wrong.  

Let's label the angles a,b,c,d,e with a being the smallest and e being the largest. a+x = b. a+2x=c. a+3x=d.a+4x=e. A is 4x, or 44 degrees smaller than E. This means x is 11. And, if you add up all the angles, you get 540 because a pentagon is 540 total degrees. 5a+110= 540. 5a= 430. a=86. The smallest angle is 86.

The answer for one of them, or the answer for two of them. For both answers to be correct, there is a 1 in 9 chance because 1/3*1/3 = 1/9.

But if you want to find the probability that one answer is right and the other is wrong is 1/3*2/3 which is 2/9. But, you have to multiply that by two because you can have the first right and the second wrong or the second right and the first wrong, so it is actually 4/9. Both answers right: 1/9, one answer right one answer wrong:4/9, Both right or one right one wrong:5/9

To fill the jug from scratch you need 3 liters of milk because 1/3 divided by 3 is 1/9. But if he already made 1/9 a jug of tea, then he needs 2 2/3 liters of milk. 3 liters per jug

I don't get it then. 11 works because 11*3 + 3*2 = 39. But 12 doesn't work because 12*3 + 2*2 =40. But 2*2+5 doesn't equal 12. Maybe 10 if the equation f <= 2S +5 is actually f < 2S +5. Is this your aops homework? Because I am doing geometry on aops, lol

Let's first just substitute the sack of flour from the second equation into the first equation. You now get 8S+10 < =40, then 8S <= 30. Then, you get

S = 3 because S = 4 won't work. If S = 3, you get 3F <= 34. One sack of flour is equal to 11.

I first abbreviated chocolate bars for cb and gummy candies for gc. I started with Cb+gc=275. I used guess and check for this one. Let's start off with 100 Chocolate bars. This amounts to 125+131.25 = 256.25. This shows that you need more chocolate bars. Each gummy candy you switch into a chocolate bar will add 0.5 dollars to your total bill. You subtracted 272.25 from 256.25, and you get 16. 16 is 32 halves of a dollar. This means you need 32 more Chocolate bars. This amounts to a total of 100+32 = 132 chocolate bars and 143 gummy candies.

When a line is parallel, the k value stays the same. The k value in this case is 4. but the 6 is subject to change. If you plug in 5 for the x and 10 for the y, the equation becomes 10 = 4*5+b. You can now see that b = -10. The equation becomes y = 4x-10. You are trying to find the x- intercept, so you plug in 0 for x and see that the y value becomes -10. The answer is -10.

Logically, you should use the 20% off coupon first. This is because if you use it first, you will cut off the highest price with it. You will cut off $8, but if you use it second, you will only cut off $7.

You should use the store coupon first and the manufacturer's coupon second for the maximum discount. If you use this way, the box will cost $27

You can multiply Danielle's amount by 4, so she has 12 TG's and 20 STGLO Fist for 224.08 dollars. Then, you can multiply Ellen's fish so she has 12 TG's and 9 STGLO Fish for 125.19 dollars. Then, you subtract them and the TG fish cancel out and you have 11 STGLO Fish for 98.89 dollars. Then you find that one STGLO Fish is 8.99 dollars by dividing it by 11. After that, u plug that into Ellen's equation by substituting the STGLO Fish with 8.99 each STGLO Fish there is. This makes the equation 4 TG  + $26.97 = $41.73. Subtract 26.97 from both sides and you get 4TG = $14.76. Divide both sides by 4 and u get 3.69 a Turquoise Guppy. The answer is 3.69 a Turquoise Guppy. Hope I helped. :)