Question

Laneka owns a cake shop.She is currently preparing cakes for two anniversary parties. The first cake has 3 small tiers and 1 medium tier and will serve a total of 100 guests. The second one has 3 small tiers and 2 medium tiers and will serve a total of 140 guests represent the situation with a system of equations

Answer 1

The system of equations are
`\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.`.

Explanation:

Let 's' represents the number of guest small tier can serve.

Let 'm' represents the number of guest medium tier can serve.

Now Given:

For First cake:

Number of small tiers = 3

Number of medium tier = 1

Total serving guest = 100

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

`3s+m=100`

For Second cake:

Number of small tiers = 3

Number of medium tier = 2

Total serving guest = 140

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

`3s+2m=140`

Hence The system of equations are
`\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.`.