Question 147690
With two variables------x=number of kilograms of 90cent peanuts and y=number of kilograms of 110cent almonds.

Set up an equation using the word problem: {{{90x+110y=98(20)}}} because the coefficients are the prices of the almonds and peanuts and the variable and 20 are the number of them.  Then set up another equation {{{x+y=20}}} because the sum of the kilograms is 20.  Then solve for x and get {{{x=20-y}}}.  Plug that in the first equation and get {{{90(20-y)+110y=98(20)}}}.  Then distribute and get {{{1800-90y+110y=1960}}}.  Combine like terms and get {{{1800+20y=1960}}}.  Subtract 1800 from both sides and get {{{20y=160}}}.  Divide both sides by 20 and get {{{y=8}}}. Then plug 8 in for y in the second equation and get {{{x+8=20}}}.  So x=12.  So 8 kilograms of 110cent almonds and 12 kilograms of 90 cent peanuts is your final answer.



With one variable------x=number of kilograms of 90cent peanuts and 20-x=number of kilograms of 110cent almonds.{{{90x+110(20-x)=98(20)}}}
Distribute and get {{{90x+2200-110x=1960}}}.  Then combine like terms and get {{{2200-20x=1960}}}. Subtract 2200 from each side and get {{{-20x=-240}}}.  Divide both sides by 20 and get {{{x=12}}}.  This is the number of kilograms of 90 cents peanuts. Then do 20-x or 20-12 and get 8. This is the number of kilograms of 110cent almonds. So 8 kilograms of 110cent almonds and 12 kilograms of 90 cent peanuts is your final answer.