(a)
To write: System of equations to model the situation.
(a)
Answer to Problem 10STP
System of equations,
For total number:
For total value:
Explanation of Solution
Given information:
Total number of quarters and dimes is 14.
Total value of all the coins is $2.75.
Let
qbe the number of quarters.
And
d be the number of dimes.
We know that
Total number of quarters and dimes is 14.
Thus,
For total number
We also know
Total value of all the coins is $2.75.
Since we do not know the number of quarters and dimes,
Thus,
For total value of coins:
(b)
To write: Matrix equation for solving d and q .
(b)
Answer to Problem 10STP
Matrix equation:
Explanation of Solution
Given information:
Total number of quarters and dimes is 14.
Total value of all the coins is $2.75.
From Part (a) result,
We have
System of equations,
For total number:
For total value:
Through the use of the system of equation,
The matrix equation becomes
(c)
Number of dimes and quarters Valeria has.
(c)
Answer to Problem 10STP
Valeria has 9 quarters and 5 dimes.
Explanation of Solution
Given information:
Total number of quarters and dimes is 14.
Total value of all the coins is $2.75.
We have
The matrix:
To know if the inverse exists,
Calculate the determinant first:
Now,
We need to proceed to the inverse of matrix because the determinant is not equal to 0.
Thus,
Then
Multiply each of the matrix equation obtained in Part (b) with inverse matrix:
Now,
Inverse matrix gets eliminated:
Perform the multiplication to find the values of q and d :
Therefore,
Valeria has 9 quarters and 5 dimes.
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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