aina, Kareem, and David have a total of $92 in their wallets. Kareem has $7 less than Raina. David has 3 times what Kareem has. How much do they have in their wallets?
Accepted Solution
A:
Answer: Kareem has $17, David has $51, Raina has $24
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Step 1: Solve this by using a system of equations. Start by changing what you're given from words into equations. Put variables in for the peoples' names. Let's say Raina = R, Kareem = K, and David = D. You will have 3 equations: 1) Raina, Kareem, and David have a total of $92 in their wallets. R + K + D (sum of all three) = 92 (total)
2) Kareem has $7 less than Raina K = R - 7 (seven less than Raina)
3) David has 3 times what Kareem has. D = 3K (three times Kareem)
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Step 2: You can solve for the values of R, K, and D using substitution. Let's put the first equation, R + K + D = 92, all in terms of one variable, so we can solve for that variable. Since both equations 2 and 3 have K in relation to one of the other variables, I will be putting equation 1 in terms of K! Do this by substitution some equation of K in for variables R and D in the first equation.
From equation 2, we know that K = R - 7. Add 7 to both sides, making R = K + 7. From equation 3, we know that D = 3K. This is already in perfect form to substitute.
Now substitute both R = K + 7 and D = 3K into the first equation. Simplify and solve for K: R + K + D = 92 (K + 7) + K + (3K) = 92 5K + 7 = 92 5K = 85 K = 17
Kareem has $17 in his wallet.
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Step 3: Now that you know K = 17, plug that into equation 3, D = 3K, and solve for how much David has: D = 3K D = 3(17) D = 51
David has $51 in his wallet.
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Step 4: Finally, plug K = 17 into equation 2, K = R - 7, to find how much Raina has: K = R - 7 17 = R - 7 R = 24