the step by step explanation gives you your answer
Step-by-step explanation:
The first step to find the gcf of 72 and 108 is to list the factors of each number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108.
We are going to make simultaneous equations. x will be our $3 ice cream and y will be our $5 ice cream
Equation1 ---- x + y = 50 (the sum of all the ice creams they sell) Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180 Since we can't solve for both variables we will put one of the variables in terms of the other. Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50) Now I am going to take equation 2 and replace the x with -y +50
3 (-y +50) + 5y = 180 Now I will use the distributive law on the 3 and what's in the parentheses: -3y + 150 + 5y = 180 Now I will combine like terms (the -3y and the 5y) 2y + 150 = 180 Now subtract 150 from both sides of the equation 2y = 30 Divide both sides by 2 and get y= 15 They sold 15 ice creams that cost $5 each Since equation 1 is x+y=50 we can replace y with 15 x + 15 = 50 Now subtract 15 from both sides x = 35 Since x represents the $3 ice creams, they sold 35 of those. Check: 35 X 3 = $105 15 x 5 = + <u>75 </u> $180
Assume that the length of the rectangle is "l" and that the width is "w".
We are given that: (1) The length is one more than twice the base. This means that: l = 2w + 1 .......> equation I (2) The perimeter is 92 cm. This means that: 92 = 2(l+w) ...........> equation II
Substitute with equation I in equation II to get the width as follows: 92 = 2(l+w) 92 = 2(2w+1+w) 92/2 = 3w + 1 46 = 3w + 1 3w = 46-1 = 45 w = 45/3 w = 15
Substitute with w in equation I to get the length as follows: l = 2w + 1 l = 2(15) + 1 l = 30 + 1 = 31
Based on the above calculations: length of base = 31 cm width of base = 15 cm
