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Chapter 6: Q51. (page 391)

Tionna has saved dimes and quarters in her piggy bank. Define the variables, and write equations to find the number of dimes and quarters. Then solve using the best method for the situation.

$4.00

25 coins

Short Answer

Expert verified

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

Step by step solution

01

Step 1. State the concept of elimination method.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

02

Step 2. Add or subtract the equations to eliminate one variable. 

Let the number of dimes be x(1 dime = $0.1) and the number of quarters be y(1 quarter = $0.25).

As per the conditions the system of equations thus formed will be:

x+y=25 鈥� (1)

0.1x+0.25y=4 鈥� (2)

Multiply equation (1) by 0.1.

0.1(x+y)=0.1脳(25)0.1x+0.1y=2.5鈥�.....鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�(3)

Note that both the equations (2) and (3) have 0.1xin same sign, therefore, variable xcan be eliminated if both equations are subtracted.

鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�0.1x+0.1y=2.5(鈭�)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�0.1x+0.25y=4炉鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆��鈭�0.15y=鈭�1.5Dividebothsidesby-0.15鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�y=10

03

Step 3. Solve for x.

Substitute 10 for yinto the equation (1) and solve for x.

x+y=25x+(10)鈭�10=25鈭�10x=15

Therefore, the number of dimes and quarters are 15 and 10 respectively.

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