Question

Roman buys seed packets for the school garden. One packet of radish seeds costs $1.75. One packet of tomato seeds costs $2.50. 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 on 32 packets of seeds. How many packets of each type of seeds did Roman buy? Use the table to guess and check.8 tomato and 24 radish 9 tomato and 23 radish 23 tomato and 9 radish 24 tomato and 8 radish

Answer 1

9 tomato and 23 radish

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Answer 2

Answer:

C.
`t=23,r=9` .

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,


`1.75r+2.5t=62.75...eqn1`

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,


`r+t=32...eqn2`

Using guess and check means we substitute into the given equation.

A) We substitute
`t=8,r=24` into both equations.


`1.75(8)+2.5(24)=62.75...eqn1`


`14+60\\e 62.75...eqn1`


`8+24=32...eqn2`

Both equations are not satisfied.

B)

We substitute
`t=9,r=23` into both equations.


`1.75(9)+2.5(23)=62.75...eqn1`


`15.75+57.5\\e 62.75...eqn1`


`9+23=32...eqn2`

Both equations are not satisfied.

C)

We substitute
`t=23,r=9` into both equations.


`1.75(23)+2.5(9)=62.75...eqn1`


`40.25+22.5 =62.75...eqn1`


`23+9=32...eqn2`

Both equations are satisfied.

Hence the solution is,


`t=23,r=9`

D) We substitute
`t=24,r=8` into both equations.


`1.75(24)+2.5(8)=62.75...eqn1`


`42+20\\e 62.75...eqn1`


`24+8=32...eqn2`

Both equations are not satisfied.