The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let 
and 
be, respectively, the number of girls and boys.
We know that 
(the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that 
(there are 61 students in total).
So, we have the system
We can use the first equation to substitute in the second
And then solve for :
For the second problem, let 
and 
be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
And you can solve it in the very same way we solved the previous one.
Answer:
a= Apple = 3
b= Banana =5
v= Lollypop=1
Step-by-step explanation:
36 is divided into 2 giving us 18
Let apple=a
Banana=b
Lollypop=c
In the first half
An apple + 3 bananas=18
a+3b=18 (1)
Second half is further divided into 2
That is,
18÷2=9
First half of the second half
3apples=9
3a=9 (2)
Second half of the second half
1 apple + 1 banana + 1 lollypop=9
a+b+c=9 (3)
a+3b=18 (1)
3a=9 (2)
a+b+c=9 (3)
From (2)
3a=9
Divide both sides by 3
a=9/3
a=3
Substitute a=3 into 1
a+3b=18
3+3b=18
3b=18-3
3b=15
Divide both sides by 3
b=15/3
=5
b=5
Substitute the value of a and b into (3)
a+b+c=9
3+5+c=9
8+c=9
c=9-8
c=1
Therefore,
a= Apple = 3
b= Banana =5
v= Lollypop=1
Answer:
C. y = 2/3 x - 2.
Step-by-step explanation:
The general form of the slope-intercept equation of a line is y = mx + c where m = the slope and (0. c) is the y-intercept.
We are given that the slope = 2/3 and the y intercept is at (0,-2) so our equation is y = 2/3 x - 2.
Properties of Logs
logb(x/y) = log<span>bx</span> - log<span>by</span>.
therefore
log5 (4/7)= log5 (4)- log5 (7)
<span>Solve log 5 (4) and log 5 (7) with the base change of the logarithm</span>
<span>log 5 4 = log 4 / log 5 </span>
Use the calculator:
<span>
<span>log 5 4 =0.8613531161
</span></span>
log 5 7 = log 7 / log 5
<span>log 5 7 =1.2090619551</span>
<span>log5 (4/7)= log5
(4)- log5 (7)=-0.347708839</span>
