Question

Bella and Heather put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes after a certain amount of time (x), in weeks, is shown by the equations below: Bella: y = 25x + 60 Heather: y = 30x + 10 After how many weeks will Bella and Heather have the same amount of money in their money boxes, and what is that amount?

 10 weeks, $10 
10 weeks, $310 
9 weeks, $310 
310 weeks, $10

Answer 1

ANSWER

10 weeks, $310

EXPLANATION

We have a system of linear equations as both equations need to be satisfied by the same ordered pair (x,y):

y = 25x + 60

y = 30x + 10

We can solve this by substitution. Since y is equal to 25x+60, we can substitute in 25x + 60 for y in the equation y=30x+10

y = 30x + 10

25x + 60 = 30x + 10

Subtract 25x from both sides

60 = 5x + 10

Subtract 10 from both sides and then divide both sides by 5

50 = 5x

x = 10

x represents time in weeks, so 10 weeks.

Find y, the amount of money, by substituting x=10 into either equation.

If we use y = 30x + 10, then

y = 30x + 10

y = 30(10) + 10

y = 300 + 10

y = 310

y = 310 implies $310 so the answer is 10 weeks, $310.

Answer 2

The time is 10 weeks, and the amount is $310. Option B is correct.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have a system of linear equations as both equations need to be satisfied by the same ordered pair (x,y):

y = 25x + 60

y = 30x + 10

We can solve this by substitution. Since y is equal to 25x+60, we can substitute in 25x + 60 for y in the equation y=30x+10

y = 30x + 10

25x + 60 = 30x + 10

Subtract 25x from both sides

60 = 5x + 10

Subtract 10 from both sides and then divide both sides by 5.

50 = 5x

x = 10

x represents time in weeks, so 10 weeks. Find y, the amount of money, by substituting x=10 into either equation.

If we use y = 30x + 10, then

y = 30x + 10

y = 30(10) + 10

y = 300 + 10

y = 310

Therefore, the time is 10 weeks, and the amount is $310. Option B is correct.

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