Free Balancing Equations Calculator - Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Let w be the number of weeks that go by for saving/spending. Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U] B(w) = Initial Amount - spend per week * w weeks B(w) = 450 - 3w Set up Betty's balance equation, B(w). Saving means we [U]add[/U] B(w) = Initial Amount + savings per week * w weeks B(w) = 120 + 8w The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w: 450 - 3w = 120 + 8w Add 3w to each side to isolate w: 450 - 3w + 3w = 120 + 8w + 3w Cancelling the 3w on the left side, we get: 450 = 120 + 11w Rewrite to have constant on the right side: 11w + 120 = 450 Subtract 120 from each side: 11w + 120 - 120 = 450 - 120 Cancelling the 120's on the left side, we get: 11w = 330 To solve for w, we divide each side by 11 11w/11 = 330/11 Cancelling the 11's on the left side, we get: w = [B]30 [MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money? We set up a balance equation B(m) where m is the number of months. [U]Set up Deon's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 650 - 40m [U]Set up Mai's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 850 - 65m When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m: 650 - 40m = 850 - 65m Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -40m and -65m. To do that, we add 65m to both sides -40m + 650 + 65m = -65m + 850 + 65m [SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE] 25m + 650 = 850 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 650 and 850. To do that, we subtract 650 from both sides 25m + 650 - 650 = 850 - 650 [SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE] 25m = 200 [SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE] 25m/25 = 200/25 m = [B]8[/B]

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take? Set up account equations A(d) where d is the number of days since time 0 for each account. Ethan A(d): 9079 + 19d Kurt A(d): 9259 + d The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other: 9079 + 19d = 9259 + d [URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B]. So in 10 days, both accounts will have equal amounts in them. Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation: A(10) = 9259 + 10 A(10) = $[B]9,269 [/B] After 10 days, both accounts have $9,269 in them.

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money? Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w): B(w) = 1200 - 40w Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w): B(w) = 120 + 50w When they have the same amount of money, we set the balance equations equal to each other: 1200 - 40w = 120 + 50w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get: w = [B]12[/B]

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain Set up the Balance account B(m), where m is the number of months since the deposit. Matt: B(m) = 20m + 100 Ben: B(m) = 80 + 30m Set both balance equations equal to each other to see if they ever have the same balance: 20m + 100 = 80 + 30m To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B100%3D80%2B30m&pl=Solve']we type this equation into our search engine[/URL] and we get: m = [B]2 So yes, they will have the same balance at m = 2[/B]

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount [U]Set up the Balance function B(w) where w is the number of weeks for Megan:[/U] B(w) = savings per week * w + Current Balance B(w) = 5.50w + 50 [U]Set up the Balance function B(w) where w is the number of weeks for Connor:[/U] B(w) = savings per week * w + Current Balance B(w) = 7.75w + 18.50 The problem asks for w when both B(w) are equal. So we set both B(w) equations equal to each other: 5.50w + 50 = 7.75w + 18.50 To solve this equation for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=5.50w%2B50%3D7.75w%2B18.50&pl=Solve'] type it in our search engine[/URL] and we get: w = [B]14[/B]

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same? Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance [LIST] [*]You --> B(w) = 18.25w + 28 [*]Your friend --> B(w) = 161 - 15w [/LIST] Set them equal to each other 18.25w + 28 = 161 - 15w [URL='http://www.mathcelebrity.com/1unk.php?num=18.25w%2B28%3D161-15w&pl=Solve']Type that problem into the search engine[/URL], and you get [B]w = 4[/B].

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance? [U]Set up the savings account S(w) for you where w is the number of weeks[/U] S(w) = 140 + 10w [U]Set up the savings account S(w) for your friend where w is the number of weeks[/U] S(w) = 95 + 19w The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other: 140 + 10w = 95 + 19w To solve this equation for w, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2B10w%3D95%2B19w&pl=Solve']we type it in the search engine[/URL] and get: w = [B]5[/B]