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

Answer:

9 tomato and 23 radish

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Answer 2

Answer:

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

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,

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

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.

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

$14+60\ne 62.75...eqn1$

$8+24=32...eqn2$

Both equations are not satisfied.

B)

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

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

$15.75+57.5\ne 62.75...eqn1$

$9+23=32...eqn2$

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.

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

$42+20\ne 62.75...eqn1$

$24+8=32...eqn2$

Both equations are not satisfied.