Question

тWrite a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Hunter and his little sister are saving up money to buy a joint birthday present for theirmother. Hunter already has $5 saved and plans to save $20 per week from his allowance. Hissister has $8 saved so far and will save $17 per week from hers. The two siblings will soonhave saved the same amount towards their mother's gift. How much will each one havesaved? How long will that take?

Answer 1

Each one will have saved $25 after 1 week

Step-by-step explanation:

If y is the amount saved and x is the number of weeks, we get that the system of equations is

y = 5 + 20x

y = 8 + 17x

Because the amount saved by Hunter will be equal to the $5 that he has added to $20 times the number of weeks and the amount saved by his sister will be equal to $8 added to $17 per week.

Then, to solve the system substitude the first equation on the second

y = 8 + 17x

5 + 20x = 8 + 17x

Solving for x, we get:

5 + 20x - 17x = 8 + 17x - 17x

5 + 3x = 8

5 + 3x - 5 = 8 - 5

3x = 3

3x/3 = 3/3

x = 1

Finally, the value of y is

y = 5 + 20x

y = 5 + 20(1)

y = 25

Therefore, each one will have saved $25 after 1 week.