Jill bought oranges and bananas. she bought 12 pieces of fruit and spent $5. oranges cost $0.50 each and bananas $0.25. write a system of equations to model the problem. then solve the system algebraically. how many oranges and how many bananas did Jill buy? show work please

Answers

Answer 1

Answer: x=number of oranges.
y=number of bananas.
$5

we can suggest this system of equations:
x+y=12
0.5x+0.25y=5
We can solve this system of equations by substitution method.
x=12-y

0.5(12-y)+0.25y=5
6-0.5y+0.25y=5
-0.25y=5-6
-0.25y=-1
y=-1 /- 0.25=4

x=12-y
x=12-4=8

Answer: Jill bought 8 oranges and 4 bananas.

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The sum of nine times a number and fifteen is less than or equal to the sum of twenty four and ten times the number

Answers

let x be the number, then
9x + 15 < or = 10x + 25
then this inequality can be solved
subtract 9x from both sides of < or =
15 < or = x + 25
subtract 25 from both sides of < or =
-10 < or = x
this can be written as
x > or = -10

The sum of nine times a number and fifteen is less than or equal to the sum of twenty four and ten times the number needs to be put down in an inequality.

$9x+15 \leq 24+10x$

Solve for x.

$-x \leq 9$
$x \geq -9$

4. Ellie uses 12.5 pounds of potatoes to make mashed potatoes. She uses one-tenth as many pounds of butter as potatoes. How many pounds of butter does Ellie use?

Answers

1.25 pounds (sorry i had to use more characters)

Amanda had $20 when she went into the shopping center. She purchased a snack to eat for $y and then bought two items at a clothing store each of which cost $x. Which expression represents the amount of money she has left after the purchases? *

Answers

x+y = 20
Expression: 20 - 2x - y (expressions don’t have equal signs)

Please help me I dont under stand these. I need help like right now.How many solutions are there to the following system of equations?

3x – 9y = 0
–x + 3y = –3

A. infinitely many
B.1
C.2
D.0
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What is the solution to the system of equations?
2x + y= -3
x - 2y= -4

(___,___)

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In a recent golf match, Tiger’s score was 4 less than Phil’s score. Their combined scores totaled 140. Let p represent Phil's score and t represent Tiger's score.

Which pair of equations can be used to determine their scores?

A. p – t = 140
p + t = 4

B. p + 140 = t
p = 4

C. p + t = 140
p – t = 4

D. p + t = 140
p + t = 4

(i think this one is C)

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The system of equations is coincident.

What are the missing values?

3x + y= 7
9x + __ y= __

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Allison and her husband Noah both get in their cars and begin to drive at the same time. Allison starts 360 mi from their home and drives directly home at a constant rate of 50 mph. Noah starts at their home and drives away from the home at a constant rate of 40 mph. The system that models this situation is given, where d represents the distance from home, and t represents time, in hours. The solution to the system is (4, 160).

What is the correct interpretation of the solution to this system?

d = 360 - 50t
d =40t

A. Noah will be 160 mi from home and Allison will be 4 mi from home.

B. Allison and Noah will both be 160 mi from home after 4 h.

C. Noah will be 4 mi from home and Allison will be 160 mi from home.

D. Allison and Noah will both be 4 mi from home when they drive for 160 min.

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