Answer:
C. [tex]t=23,r=9[/tex] .
Step-by-step explanation:
Let r represent the cost of one packet of radish seeds and let t represent the cost of one packet of tomato seeds.
Roman spent $62.75
This implies that,
[tex]1.75r+2.5t=62.75...eqn1[/tex]
Roman bought 32 packets of seeds and one packet of radish seeds costs
$ 1.75.
One packet of tomato seeds costs $ 2.50.
This implies that,
[tex]r+t=32...eqn2[/tex]
Using guess and check means we substitute into the given equation.
A) We substitute [tex]t=8,r=24[/tex] into both equations.
[tex]1.75(8)+2.5(24)=62.75...eqn1[/tex]
[tex]14+60\ne 62.75...eqn1[/tex]
[tex]8+24=32...eqn2[/tex]
Both equations are not satisfied.
B)
We substitute [tex]t=9,r=23[/tex] into both equations.
[tex]1.75(9)+2.5(23)=62.75...eqn1[/tex]
[tex]15.75+57.5\ne 62.75...eqn1[/tex]
[tex]9+23=32...eqn2[/tex]
Both equations are not satisfied.
C)
We substitute [tex]t=23,r=9[/tex] into both equations.
[tex]1.75(23)+2.5(9)=62.75...eqn1[/tex]
[tex]40.25+22.5 =62.75...eqn1[/tex]
[tex]23+9=32...eqn2[/tex]
Both equations are satisfied.
Hence the solution is,
[tex]t=23,r=9[/tex]
D) We substitute [tex]t=24,r=8[/tex] into both equations.
[tex]1.75(24)+2.5(8)=62.75...eqn1[/tex]
[tex]42+20\ne 62.75...eqn1[/tex]
[tex]24+8=32...eqn2[/tex]
Both equations are not satisfied.
