Afamily went to an amusement park and paid $12 for each adult and $8 for each child. a group of 15 people went to the park and it cost $140. this system of equations models this situation, where x is the number of adults and y is the number of children.
how many children were in the group?
x + y = 15
12x + 8x = 140

Yes, very good. correct equations
now simplify the second equation
12x+8y=140
undistribute the 4 in both 8 and 12
4(3x+2y)=140
divide both sides by 4
2x+3y=35

seconde equation
x+y=15
multiply by 2
2x+2y=30

compare
2x+3y=35
2x+2y=30
make the secondn one negative and add
2x+3y=35
-2x-2y=-30  +
0x+1y=5
y=5
subsiutte
x+y15
x+5=15
subttract 5
x=10

10 adults
5  kides

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.