Solve for the following system of equations using substitution, what is the value of y? 2x 3y=105 x 2y=65
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Answer:
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
Step-by-step explanation:
1) The initial number of signatures Mimi has = 30 Signatures
The average rate at which Mimi can collect signatures = 8 signatures per hour
The average rate at which Rita can collect signatures = 14 signatures per hour
The table of values showing the number of signatures Mimi and Rita can have at a given hour is presented as follows;
For Mimi, we have;
Hour Number of Signatures
0 30
1 38
2 46
3 54
4 62
5 70
For Rita, we have;
Hour Number of Signatures
0 0
1 14
2 28
3 42
4 56
5 70
2) The equation representing the number of signatures Mimi has at a given time, t, is given as follows;
The number of signatures Mimi has = 30 + 8 × t
The equation representing the number of signatures Rita has at a given time, t, is given as follows;
The number of signatures Rita has = 14 × t
3) Please find attached the required graph of the number of signatures Mimi and Rita has
4) The solution if the system of equations is given as follows;
30 + 8 × t = 14 × t
From which we have;
30 = 14 × t - 8 × t = 6 × t
t = 30/6 = 5 Hours
By substituting t = 5 hours in the above equations, the equal number of signature of signatures Mimi and Rita can have is therefore;
30 + 8 × 5 = 70 signatures = (14 × 5) signatures
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
5) The meaning of the solution is that is Mimi and Rita continue collecting signatures at their respective constant rate of 8 and 14 signatures per hour, given that Mimi already has 30 signatures, they will have the same number of 70 signatures after 5 hours
