Terry bought some gum and some candy. The number of packs of chewing gum was one more than the number of mints. The number of mints was three times the number of chocolate bars. If gum cost 6 cents a pack, mints cost 3 cents each, and chocolate bars cost 10 cents each, how many of each confection did he get for 80 cents?

number of packs of chewing gum is 7

number of mints  is 6

number of chocolate bars is 2

Step-by-step explanation:

number of packs of chewing gum → x,  cost 6¢

number of mints → y = x-1 =3z,  cost  3¢

number of chocolate bars → z = y/3 = (x-1)/3, cost 10¢

put in equation 6x + 3y +10z = 80 plug in term of x

6x +3(x-1) +10((x-1)/3) =80 multiply each side by 3

18x +9(x-1) +10(x-1) =240 distribute

18x+9x-9+10x-10 =240 combine like terms

37x-19 = 240 add 19 in each side

37x =259

x = 7

plug into y = x-1 = 7-1 = 6 so y=6

and  z = y/3 =6/3 =2 so z = 2

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

answer: 8d

step-by-step explanation:

45+5= 50+5=55+5=60