Answer:
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Number of cards of John: J
Number of cards of Alan: A
<span>John and Alan have a collection of x baseball cards:
J+A=x (1)
</span>John has x/4 cards:
J=x/4
<span>What fraction of the cards does Alan have?
</span>
Replacing J by x/4 in the equation (1)
(1) J+A=x
x/4+A=x
Solving for A:
x/4+A-x/4=x-x/4
A=4x/4-x/4
A=(4x-x)/4
A=3x/4
Answer: Alan has 3/4 of the cards
Let us evaluate the given statements.
A, A number is divisible by 9 if and only is it ends in 3.
23/9 is not divisible.
FALSE
B. A quadrilateral is a square if and only if it has four right angles.
A rectangle is a quadrilateral with four right angles, but it is not a square.
FALSE
C. The sum of two integers is positive if and only if the two integers are
positive.
12 + (-10) = 2 (positive).
FALSE
D. A number is an even number if and only if it is divisible by 2.
Thi is true by definition.
TRUE
Answer: D
