SOLUTION: Abu came out of the bakery shop after spending RM 320 on carrot cakes, cheese cakes and chocolate cakes for his school’s Canteen Day. Altogether, he bought 21 cakes. The prices

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Abu came out of the bakery shop after spending RM 320 on carrot cakes, cheese cakes and chocolate cakes for his school’s Canteen Day. Altogether, he bought 21 cakes. The prices      Log On


   

Question 1184544: Abu came out of the bakery shop after spending RM 320 on carrot cakes, cheese cakes
and chocolate cakes for his school’s Canteen Day. Altogether, he bought 21 cakes. The
prices for each carrot cake, cheese cake and chocolate cake are RM 10, RM 20 and RM
15 respectively. The number of chocolate cakes bought was twice the total number of
carrot and cheese cakes. By using inverse matrix method, find how many each type of
cakes that Abu has bought.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = # of carrot cakes, y = # of cheese cakes, and z = # of chocolate cakes.

===> The system is system%28matrix%283%2C1%2C+x%2By%2Bz+=+21%2C+10x%2B20y%2B15z+=+320%2C+z+=+2x%2B2y%29%29, or system%28matrix%283%2C1%2C+x%2By%2Bz+=+21%2C+2x%2B4y%2B3z+=+64%2C+2x%2B2y-z=0%29%29, or equivalently.

===> .

I now refer you to https://www.emathhelp.net/calculators/linear-algebra/inverse-of-matrix-calculator/,
where the inverse of the above matrix can be calculated with all steps shown.

===> .

The number of each type of cake bought is now clear.