Question

someone help me on this! :D the sum of two numbers is -1. when twice the first number and four times the second number are added, the sum is -10. what are the two numbers?

Answer 1

You have 2 equations. First being x+y = -1 and 2x+4y=-10. Take either one and isolate one variable. Say, x= -1-y then sub it into the second equation 2(-1-y)+4y = -10. Solve for y where -2-2y+4y=-10 which gives y=-4. Sub in y value into either equation to find x. x+(-4) = -1 so x=3. Sub into second equation to double check.

Answer 2

do you think you can help me with two more problems?

Answer 3

if it's similar, I guess.. depends on what kinds of question it is...

Answer 4

okay heres the first one,
Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max's family spent $146 on 3 adult tickets and 2 youth tickets. what is the price of a youth ticket?

Answer 5

?

Answer 6

It's basically the same as above, method wise. So you have 2 equations. Let a = adult tickets and y be youth tickets. 1) 2a+3y = 134 and 2) 3a+2y = 146. Isolate for one of the equations such that you are isolating in terms of y since you are only looking for youth. so you would have a= 1/2(134-3y) and sub it into second eq so you would have 3[1/2(134-3y)+2y = 146. Collect like terms and isolate for y and you would have the price for y. You can check if your answer is correct by finding a by subbing y value into one of the equations and then with both values, check if it equals to the given costs.

Answer 7

do you want the second now?

Answer 8

sure

Answer 9

carl bought 19 apples of 2 different varieties to make a pie. the total cost of the apples was $5.10. granny smith apples cost $0.25 each and gala apples cost $0.30 each. how many of each type of apple did carl buy?

Answer 10

Let a= granny smith and b= gala. 2 equations again. 1) a+b=19 2)0.25a+0.30b = 5.10
Isolate one of the variables such as a=19-b and sub into second eq so 0.25(19-b) +0.3b = 5.10. Expand, collect like terms and solve for b. Now, you would have your number of gala apples. sub it back into the first equation and you would get your number of granny smith.

Answer 11

will you help me with the brianna problem, i don't know how to simplify and get the answers. well i hate fractions

Answer 12

I'd like to propose a different way of solving the brianna problem. It minimizes the need of fractions.

As babalooo said, 2a+3y = 134 and 3a+2y = 146. Multiply each equation by the coefficient of a in the other equation: 3(2a+3y) = 3(134) and 2(3a+2y) = 2(146); 6a+9y = 402 and 6a+4y = 292. Subtract the second equation from the first: (6a+9y)-(6a+4y) = 402-292; 5y = 110; y = 22.

Answer 13

I'd also like to propose a more verbal solution.

Consider the composition of both families. The only difference is that Max's has one youth swapped out for an adult. This makes the price $146-$132 = $12 higher, so the adult ticket is $12 more expensive than the youth ticket. Notice also that both families, 5 youths and 5 adults altogether, paid a total of $134+$146 = $280. This means the price of one youth ticket and one adult ticket is $280/5 = $56. Should you swap the adult ticket out for a youth ticket, the price would go down by $12 and you would pay $56-$12 = $44 for two youth tickets. If you buy half as many, you pay half as much: $44/2 = $22 for one youth ticket.