Mathematics, 05.10.2019 03:50 davidgritz2006

Jimmy set his score for his math test. after the math teacher returnee his paper to him, he realized that if he increased his target by 10%, he would need 1 more mark to reach his actual score. if he increased his target by 15%, this target would exceed his actual test marks by 3. what is his actual test score.

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When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89

Answer from: Quest

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

Answer from: Quest

the speed is $135$ miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

$y/x=k$

for the point $(1.5,90)$

substitute the values of x and y

$k=90/1.5=60\ miles/hour$

the linear equation is equal to

$y=60x$

statements

case a) it takes $2$ hours to go $120$ miles

the statement is true

because

substitute

for $x=2$

find the value of y in the linear equation

$y=60(2)=120\ miles$ > is correct

case b) the speed is $135$ miles per hour

the statement is false

because the speed is $60\ miles/hour$

case c) the unit rate for the trip is $60\ miles/hour$

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took $20$ minutes to go the first $20$ miles

the statement is true

because

substitute

for $x=20\ minutes=(1/3)\ hour$

find the value of y in the linear equation

$y=60(1/3)=20\ miles$ > is correct

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