Math HELP plz-solving word equations?

Question

I am having troubles with these word equation. could someone show me how to solve this
Q: At Jennas Bistro the server earns $90/d and the cook earns $140/d, of all the tips collected the server gets .75% and the cook gets .25%. How much would have to be receieved in tips for the server and the cook to earn the same amount for one day's work.

The equations i got is:
let y represent amount earned in 1 day
let x reprent amount of tips

server: y=.75x+90 cook, y=.25x+140

the problem comes when i solve the eqaution by putting one into the other

Answer 1

Set the two equations equal to each other:

.75x + 90 = .25x + 140

You set the equations up nicely. They represent how much each person makes per day. Since you know that you want those amounts to equal each other you can set the equations equal to each other and then find out what x would have to be to make this true.

so:

.50x = 50
x = 100 (dollars in tips)

Answer 2

since you want the y's to be equal, set the two equations equal to each other and solve for x.
.75x + 90 = .25x + 140
.50x = 50
x = 50/.50 = 100
so the total tips is $100. then the server makes 90 + 75 = $165 and the cook makes 140 + 25 = $165

Answer 3

Suppose T is the total tips. The the server takes home 90+0.75T and the cook takes home 140+0.25T. If they are equal then

90 + 0.75T = 140 + 0.25T

Subtract 90 from both sides, subtract 0.25T from both sides, to get

0.5T = 50

Double both sides to get

T = 100

So the total tips has to be 100 dollars. As a check, the server then gets 90+75 = 165 dollars and the cook gets 140 + 25 = 165 dollars, which is the same

Answer 4

Let x be the tips required for the server and the cook to earn equally.

90+x(75%) = 140+x(25%)

Solve for x,
x = $100

Answer 5

Your equations are correct. Here's how to find x

server=.75x+90
cook=.25x+140

Since you want to see what x must be for their wages to be equal, you make the to equations equal to each other

.75x + 90 = .25x + 140

then using simple algebra, you get:
.5x = 50
x = 100

Therefore, $100 in tips must be collected for the cook and the server to have equal wages for that day.

Answer 6

a million) i will call the dimensions of an ingredient of your unique sq. L. you recognize that the dimensions of one fringe of your rectangle is L + 5, and the dimensions of the different area is L + 2. You multiply those values mutually to get the area of the rectangle (one hundred thirty m^), so: (L + 5)(L + 2) = one hundred thirty Multiply this out: L^ + 5L +2L + 10 =one hundred thirty Simplify: L^ + 7L - a hundred and twenty = 0 Use the quadratic equation or ingredient to remedy for L. L = -15 or L=8. because of the fact this might properly be a real-international project, you like the beneficial value for L (L=8). 2) I continuously think of it facilitates to entice my triangles and label the components. i will call the fast leg of the the terrific option triangle X. you already know that the hypotenuse is 13 cm, and the the rest area is X + 7. you could positioned those values immediately into the Pythagorean theorem: X^ + (X + 7)^ = 13^ X^ + (X +7)(X + 7) = 169 X^ + X^ + 7X + 7X + 40 9 = 169 2X^ + 14X - a hundred and twenty =0 X=5 or X=-12 because of the fact it is yet another genuine-existence occasion, you recognize which you particularly desire the beneficial value of X (X=5), and that permits you to remedy for the different area: 5 + 7 = 12 So the components of your triangle are 5cm, 12cm, and 13cm.