Let the prices (in dollars) for each size of print be S, M, L for small, medium and large prints.
Let B=base price in dollars. So for each set:
Set A: B+L+3M+5S=19.75
Set B: B+3L+5M+8S=32.75
Set C: B+5L+8M+15S=49
Also, B=2L, so the equations become:
3L+3M+5S=19.75,
5L+5M+8S=32.75,
7L+8M+15S=49.
To solve using matrices and Cramer's method, first evaluate the determinant, made up of the coefficients of the variables, Δ=
| 3 3 5 |
| 5 5 8 | = 3(75-64)-3(75-56)+5(40-35)=33-57+25=1.
| 7 8 15 |
Now evaluate this determinant, which replaces the L coefficients with the constants, ΔL=
| 19.75 3 5 |
| 32.75 5 8 | = 19.75(75-64)-3(491.25-392)+5(262-245)=217.25-297.75+85=4.5.
| 49.00 8 15 |
From L=ΔL/Δ=$4.50.
Similarly, ΔM=
| 3 19.75 5 |
| 5 32.75 8 | = 3(491.25-392)-19.75(75-56)+5(245-229.25)=297.75-375.25+78.75=1.25.
| 7 49.00 15 |
M=ΔM/Δ=$1.25.
And ΔS=
| 3 3 19.75 |
| 5 5 32.75 | = 3(245-262)-3(245-229.25)+19.75(40-35)=-51-47.25+98.75=0.50.
| 7 8 49.00 |
S=ΔS/Δ=$0.50.
B=2L=$9.
SOLUTION
Base price is $9; small photo=$0.50; medium photo=$1.25; large photo=$4.50.