The table shows Marco’s checking account
activity for the first week of June.
a. Marco wants his total deposits for the month of June
to exceed $1,500. Write and solve an inequality to find
how much more he needs to deposit to meet this goal.
b. Marco wants his total purchases for the month to be less than $450.
Write and solve an inequality to find how much more he can spend
and still meet this goal.
c. There are three weeks left in June. If Marco spends the same amount in
each of these weeks that he spent during the first week, will he meet his
goal of spending less than $450 for the entire month? Justify your answer.
Deposit – Paycheck $520.45
Purchase – Grocery Store $46.50
Purchase – Movie Theatre $24.00
Purchase – Water bill $22.82
I know for a that it has to do something with adding them all together, but my answer of 520.45+46.50+24+22.82 ≤ m m=total money
I feel this isn't correct.
Well, you're on the right track with adding the amounts together, but your inequality is a bit off. Let's break it down:
a. To find how much more Marco needs to deposit to meet his goal of exceeding $1,500, we can set up the inequality as follows:
520.45 + x > 1500
Here, x represents the additional amount Marco needs to deposit. To solve the inequality, subtract 520.45 from both sides:
520.45 - 520.45 + x > 1500 - 520.45
x > 979.55
So, Marco needs to deposit more than $979.55 to meet his goal.
b. To determine how much more Marco can spend and still meet his goal of total purchases being less than $450, we can set up the inequality:
46.50 + 24.00 + 22.82 + x < 450
Here, x represents the additional amount Marco can spend. To solve the inequality, subtract the sum of the purchases from both sides:
46.50 + 24.00 + 22.82 + x - 46.50 - 24.00 - 22.82 < 450 - 46.50 - 24.00 - 22.82
x < 334.68
So, Marco can spend up to $334.68 more and still meet his goal.
c. If Marco spends the same amount in each of the remaining three weeks as he did in the first week, we can find the total amount he will spend. Adding up the purchases from the first week, we get:
46.50 + 24.00 + 22.82 = 93.32
If Marco spends the same amount each week, he will spend 93.32 * 3 = 279.96 for the remaining weeks. Adding this to the purchases from the first week, we get:
279.96 + 93.32 = 373.28
Since 373.28 is less than $450, Marco will still meet his goal of spending less than $450 for the entire month.
Hope this helps!
To solve these problems, we need to keep track of the total deposits and total purchases for the month of June. Let's go step by step:
a. To find how much more Marco needs to deposit to meet his goal of exceeding $1,500 in total deposits for the month of June, we need to add up all his deposits so far and compare it to the goal amount:
Total deposits for June = $520.45
Therefore, the inequality can be written as:
Total deposits ≤ $1,500
To find out how much more Marco needs to deposit to meet the goal, we can subtract the total deposits so far from the goal:
$1,500 - $520.45 = $979.55
Therefore, Marco needs to deposit at least $979.55 more to meet his goal.
b. To find out how much more Marco can spend and still meet his goal of total purchases being less than $450 for the month, we need to subtract the total purchases so far from the goal amount:
Total purchases for June = $46.50 + $24.00 + $22.82 = $93.32
Therefore, the inequality can be written as:
Total purchases ≤ $450
To find out how much more Marco can spend, we can subtract the total purchases so far from the goal:
$450 - $93.32 = $356.68
Therefore, Marco can spend up to $356.68 more and still meet his goal.
c. To answer this question, we need to consider if Marco's spending pattern in the first week will allow him to stay within his goal of spending less than $450 for the entire month.
Total purchases for the first week = $46.50 + $24.00 + $22.82 = $93.32
To determine if he will meet his goal for the entire month, we need to multiply his current weekly spending by the number of remaining weeks and compare it to his goal:
Total purchases for entire month = $93.32 x 3 = $279.96
Since $279.96 is less than $450, Marco will meet his goal of spending less than $450 for the entire month if he continues to spend the same amount each week.
To find the total deposits for the month of June, you need to add up all the deposits that Marco made during the first week. In the given table, there is only one deposit mentioned, which is his paycheck of $520.45.
So, the total deposits for the month of June would be the same as the deposit for the first week, which is $520.45.
To determine how much more Marco needs to deposit in order to exceed $1,500, you can set up an inequality. Let's use the variable "d" to represent the additional deposit amount Marco needs.
The inequality would be:
520.45 + d > 1500
To solve for "d", you subtract 520.45 from both sides of the inequality:
d > 1500 - 520.45
d > 979.55
So, Marco needs to deposit more than $979.55 to meet his goal of total deposits exceeding $1,500 for the month of June.
Now, let's move on to part b.
To find out how much more Marco can spend and still meet his goal of total purchases being less than $450, you need to subtract the total purchases for the first week from $450.
The total purchases for the first week are:
46.50 + 24.00 + 22.82 = $93.32
Let's use the variable "x" to represent the additional amount Marco can spend.
The inequality would be:
93.32 + x < 450
To solve for "x", you subtract 93.32 from both sides of the inequality:
x < 450 - 93.32
x < 356.68
So, Marco can spend an additional amount less than $356.68 and still meet his goal of total purchases being less than $450 for the month of June.
Moving on to part c, to check if Marco will meet his goal of spending less than $450 for the entire month if he spends the same amount in each of the three remaining weeks, you first need to find out how much he spent in the first week.
The total purchases for the first week are:
46.50 + 24.00 + 22.82 = $93.32
Assuming he spends the same amount in each of the remaining three weeks, the total purchases for the month would be:
93.32 + 93.32 + 93.32 = $279.96
Since $279.96 is less than $450, Marco will meet his goal of spending less than $450 for the entire month if he spends the same amount in each of the remaining three weeks.