Algebra 2

1st Edition

ISBN: 9780078884825

Author: McGraw-Hill/Glencoe

Publisher: Glencoe/McGraw-Hill School Pub Co

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Question

Chapter 4.6, Problem 12CYU

To determine

To find: the number of quarters and dimes Kevin have.

Expert Solution & Answer

Answer to Problem 12CYU

The number of quarters and dimes are 10 and 15 respectively..

Explanation of Solution

Given information:

Kevin had 25 quarters and dimes.

The total value of all the coins is $$4$ .

Formula used:

Inverse of a $2×2$ matrix $A=[abcd]$ is $A−1=1ad−bc[d−b−ca]$ is, where $ad−bc≠0$ .

The value of a second order determinant is the difference of the products of the products of the two diagonals.

Steps to solve the equations are:-

Step1. Find the inverse of the coefficient matrix.

Step 2. Multiple each side of the matrix equation by the inverse matrix.

Calculation:

According to the question ,

Let x be the number of quarters .

And y be the number of dimes.

Thus, the system of equation formed is

$x+y=250.25x+0.10y=4$

The matrix equation is

$[110.250.10].[xy]=[254]$ .

Step 1.

$=A−1=1(1)(0.10)−(1)(0.25)[0.10−1−0.251]$

$=10.10−0.25[0.10−1−0.251]=−10.15[0.10−1−0.251]$

Step2.

$=−10.15[0.10−1−0.251][110.250.10].[xy]=−10.15[0.10−1−0.251][254]=[1001][xy]=−10.15[(0.10×25)+(−1×4)(−0.25×25)+(1×4)]=[1001][xy]=−10.15[2.5−4−6.25+4]=[xy]=−10.15[−1.5−2.25]$

$=[xy]=[1015]$

Thus, the number of quarters are 10 and number of dimes are 15.

Chapter 4.6, Problem 11CYU

Chapter 4.6, Problem 13PPS

Chapter 4 Solutions

Algebra 2

Ch. 4.1 - Prob. 1ACYP Ch. 4.1 - Prob. 1BCYP Ch. 4.1 - Prob. 2CYP Ch. 4.1 - Prob. 3CYP Ch. 4.1 - Prob. 1CYU Ch. 4.1 - Prob. 2CYU Ch. 4.1 - Prob. 3CYU Ch. 4.1 - Prob. 4CYU Ch. 4.1 - Prob. 5CYU Ch. 4.1 - Prob. 6CYU

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