1. Let's represent the number of video games Josh has with the variable "J".
The number of video games Will has is 3 times as many as Josh's, minus 2. So we can write the equation as:
Will's video games = 3J - 2
Since Will has 20 video games, we can substitute that into the equation:
20 = 3J - 2
To solve the equation, we can add 2 to both sides:
20 + 2 = 3J
22 = 3J
Finally, we divide both sides by 3 to solve for J:
22/3 = J
J ≈ 7.33
Therefore, Josh has around 7.33 video games.
2. Let's represent the cost of one soda with the variable "S".
The total cost of 5 sodas is equal to the cost of 3 sodas plus $7. We can write the equation as:
5S = 3S + 7
To solve the equation, we can subtract 3S from both sides:
5S - 3S = 7
2S = 7
Finally, we divide both sides by 2 to solve for S:
2S/2 = 7/2
S ≈ 3.50
Therefore, the cost of one soda is around $3.50.
3. Let's represent the number of hours Katherine worked last month with the variable "L".
The total number of hours Katherine worked this month is equal to 5 times the number of hours she worked last month, plus 3. We can write the equation as:
60 = 5L + 3
To solve the equation, we can subtract 3 from both sides:
60 - 3 = 5L
57 = 5L
Finally, we divide both sides by 5 to solve for L:
57/5 = L
L ≈ 11.40
Therefore, Katherine worked around 11.40 hours last month.
4. Let's represent the number of weeks it will take for Matt to save $15,000 with the variable "W".
Matt saves $20 each week, so the total amount saved in W weeks is equal to $20 times W. We can write the equation as:
20W = 15000
To solve the equation, we divide both sides by 20:
20W/20 = 15000/20
W = 750
Therefore, it will take Matt 750 weeks to save $15,000.
5. Let's represent the purchase cost before shipping with the variable "P".
The shipping fee is 7% of the purchase cost, so we can write the equation as:
0.07P = 30.25
To solve the equation, we divide both sides by 0.07:
0.07P/0.07 = 30.25/0.07
P = 432.14
Therefore, the purchase price before shipping was added is $432.14.