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A baker makes apple tarts and apple pies each day. Each tart, [tex]\( t \)[/tex], requires 1 apple, and each pie, [tex]\( p \)[/tex], requires 8 apples. The baker receives a shipment of 194 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

A.
[tex]\[ t \leq 40 \][/tex]
[tex]\[ p \leq 184 \][/tex]

B.
[tex]\[ t \leq 40 \][/tex]
[tex]\[ 8p \leq 184 \][/tex]

C.
[tex]\[ t \leq 40 \][/tex]
[tex]\[ p + 8t \leq 184 \][/tex]

D.
[tex]\[ t \leq 40 \][/tex]
[tex]\[ 8p + t \leq 184 \][/tex]

Sagot :

GinnyAnswer
To find the possible number of pies and tarts the baker can make, given the conditions, we need to develop a system of inequalities that represent these constraints:

1. Each tart, [tex]\( t \)[/tex], requires 1 apple, and each pie, [tex]\( p \)[/tex], requires 8 apples.
2. The baker receives a shipment of 194 apples each day.
3. The baker makes no more than 40 tarts per day.

First, let's consider the total number of apples used by the tarts and the pies. The total usage can be expressed as:
[tex]\[ t + 8p \leq 194 \][/tex]
This inequality ensures that the combined number of apples used by tarts and pies does not exceed the available 194 apples.

Next, we need to consider the constraint on the number of tarts the baker can make each day:
[tex]\[ t \leq 40 \][/tex]
This inequality ensures that the number of tarts does not exceed 40 on any given day.

Combining these inequalities, we have the following system:

[tex]\[ t \leq 40 \][/tex]
[tex]\[ t + 8p \leq 194 \][/tex]

Thus, the correct system of inequalities that can be used to find the possible number of pies and tarts the baker can make is:

[tex]\[ t \leq 40 \][/tex]
[tex]\[ t + 8p \leq 194 \][/tex]

Therefore, the correct option is:
[tex]\[ t \leq 40 \][/tex]
[tex]\[ t + 8 p \leq 184 \][/tex]
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