Question

Garima owns a cafe that serves burgers, samosas, and juice bottles. on a particular day, 100 items in total were sold. the number of burgers sold was thrice the number of samosas sold. also, the number of samosas sold was 10 more than the number of juice bottles sold.

(i) form a set of simultaneous equations for the above information.
(ii) solve the set of equations formed in (i) by matrix method.
(iii) hence, find the number of items sold in each category.

Answer 1

i) A set of simultaneous equations is b=66.

ii) The set of equations formed in by matrix method is s=22.

iii) The number of items sold in each category is j=12.

To make significant progress in solving this system of linear equations problems. Let's solve the following system of equations:

100=b+s+j

b=3s

s=j+10

We can solve the system of equations using elimination.

Steps to solve:

1. Rearrange terms in standard form:

-b-s-j=-100

b-3s=0

s-j=10

2. Eliminate s:

-b-s-j=-100

-4s-j=-100

s-j=10

3. Add the top and bottom equations:

-5j=-60

4. Solve for j:

j=12

5. Substitute j back into the top equation:

-b-s-12=-100

-b-s=-88

6. Solve for s:

-b-s=-88

s=22

7. Substitute s back into the equation b = 3s:

b=3(22)

b=66

Answer:

b=66

s=22

j=12