Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value
of $13.10. The number of quarters was 15 more than 3 times the number of dimes. How many quarters and how many dimes did Peter have?
2 answers:
Peter had 48 quarters and 11 dimes
<h3>Further explanation</h3>Simultaneous Linear Equations could be solved by using several methods such as :
- <em>Elimination Method</em>
- <em>Substitution Method</em>
- <em>Graph Method</em>
If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.
Let us tackle the problem!
Let :
<em>Number of quarters ( 25 cent coins ) = x</em>
<em>Number of dimes ( 10 cent coins ) = y</em>
<em>When he counted his quarters and dimes, he found they had a total value of $13.10.</em>
<h2>0.25x + 0.10y = 13.10</h2><em>The number of quarters was 15 more than 3 times the number of dimes.</em>
<h2>x = 15 + 3y</h2>If we would like to use the Substitution Method , then second equations above could be substituted into first equations.
0.25x + 0.10y = 13.10
0.25 (15 + 3y) + 0.10y = 13.10
3.75 + 0.75y + 0.10y = 13.10
0.85y = 13.10 - 3.75
0.85y = 9.35
y = 9.35 / 0.85
<h3>y = 11</h3>At last , we could find the value of x by substituting this y value into one of the two equations above :
x = 15 + 3y
x = 15 + 3(11)
x = 15 + 33
<h3>x = 48</h3><h3>Learn more</h3>- Perimeter of Rectangle : brainly.com/question/12826246
- Elimination Method : brainly.com/question/11233927
- Sum of The Ages : brainly.com/question/11240586
Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations
Answer: Peter had 48 quarters and 11 dimes.
Step-by-step explanation:
Let be "q" the number of quarters and "d" the number of dimes.
We know that $13.10 in cents is 1,310 cents. Then, we can set up the following system of equations:
Applying the Substitution method, we can substitute the second equation into the first one and solve for "d":
Finally, we must substitute the value of "d" into the second equation to find the value of "q". Then:
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Answer:
1. Null hypothesis:
Alternative hypothesis: Not all the means are equal
2. D. 36
3. C. 34
4. B. 1.059
5. B. 8.02
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
Part 1
The hypothesis for this case are:
Null hypothesis:
Alternative hypothesis: Not all the means are equal
Part 2
In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.
If we assume that we have groups and on each group from
we have
individuals on each group we can define the following formulas of variation:
And we have this property
We need to find the mean for each group first and the grand mean.
If we apply the before formula we can find the mean for each group
,
,
. And the grand mean
Now we can find the sum of squares between:
Each group have a sample size of 4 so then
The degrees of freedom for the variation Between is given by , Where k the number of groups k=3.
Now we can find the mean square between treatments (MSTR) we just need to use this formula:
D. 36
Part 3
For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.
And the degrees of freedom are given by:
. N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.
And now we can find the mean square within treatments:
C. 34
Part 4
The test statistic F is given by this formula:
B. 1.059
Part 5
The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.
And we can use excel to find this critical value with this function:
"=F.INV(1-0.01,2,9)"
And we will see that the critical value is
B. 8.02