SOLUTION: 2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UNKNOWNS Jaymerson's Peanut place has two types of peanut butter. Mr.Peanut, which sells for P2 per gram a

Question 1122283: 2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UNKNOWNS
Jaymerson's Peanut place has two types of peanut butter. Mr.Peanut, which sells for P2 per gram and King Peanut, which sells for P7 per gram. How many grams of each type of peanut butter must Jaymerson mix to create 20 grams of sir Peanut that will sell for P4 per gram?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the number of grams of mr. peanut.
let y = the number of grams of king peanut.

mr. peanut sells for P2 per gram.
king peanut sells for P7 per gram.

how many grams of each type of peanut butter must janmerson mix to create 20 grams of peanuts that will sell for 4 P per gram.

you have 2 equations that need to be solved simultaneously.

the first equation is x + y = 20.

this says that the total grams of sir peanut and king peanut must be equal to 20.

the second equation is 2x + 7y = 4 * (x + y)

this says that the 2 * the number grams of sir peanut + 7 * the number of of king peanut is equal to 4 * (the number of grams of sir peanut and king peanut combined).

the 2 equations that need to be solved simultaneously are:

x + y = 20
2x + 7y = 4 * (x + y)

since x + y = 20, the second equation can be simplified to:

2x + 7y = 4 * 20 which can be further simplified to:

2x + 7y = 80

the two equations to be solved simultaneously now are:

x + y = 20
2x + 7y = 80

multiply both sides of the first equation by 2 and leave the second equation as is to get:

2x + 2y = 40
2x + 7y = 80

subtract the first equation from the second to get:

5y = 40

solve for y to get y = 40 / 5 = 8.

since x + y = 20, this means that x must be equal to 20 - 8 = 12.

you have x = 12 and y = 8

you need 12 grams of sir peanut and 8 grams of king peanut to get a mix that will be priced at P4 per gram.

to see if this is correct, go back to the original equations and replace x with 12 and y with 8.

x + y becomes 12 + 8 which is equal to 20, so that part is ok.

2x + 7y = 4 * (x + y) becomes 2 * 12 + 7 * 8 = 4 * 20 which becomes 24 + 56 = 80 which becomes 80 = 80, so that part is ok.

the solution looks good.

you need 12 grams of sir peanut that sells for P2 per gram and 8 grams of king peanut that sells for P7 per gram to make a mix that will sell for P4 per gram.
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